Algebra QBA 1 Review
Short Answer
1. Juan scored 26 points in the first half of the
basketball game, and he scored n points in the
second half of the game. Write an expression to
determine the number of points he scored in all.
Then, find the number of points he scored in all if
he scored 18 points in the second half of the game.
2. Salvador has saved 130 sand dollars and wants to
give them away equally to n friends. Write an
expression to show how many sand dollars each of
Salvador’s friends will receive. Then, find the total
number of sand dollars each of Salvador’s friends
will get if Salvador gives them to 10 friends.
3. Isabel reads 15 books from the library each month
for y months in a row. Write an expression to show
how many books Isabel read in all. Then, find the
number of books Isabel read if she read for 12
months.
4. Solve
. Check your answer.
5. Solve
. Check your answer.
6. Solve –14 + s = 32.
7. A toy company's total payment for salaries for the first two months of 2005 is $21,894. Write and solve an
equation to find the salaries for the second month if the first month’s salaries are $10,205.
8. The range of a set of scores is 23, and the lowest
score is 33. Write and solve an equation to find the
highest score. (Hint: In a data set, the range is the
difference between the highest and the lowest
values.)
9. Solve
. Check your answer.
10. Solve 3n = 42. Check your answer.
11. Solve
12. Solve
13. Solve
14. Solve
.
15. Devon pays $24.95 for her roller skates. After that
she pays $3.95 for each visit to the roller rink. What
is the greatest number of visits she can afford if the
total amount she spends cannot be more than
$76.30?
16. The formula
gives the profit p when a
number of items n are each sold at a cost c and
expenses e are subtracted. If
,
,
and
, what is the value of c?
.
.
17. Solve
18. Solve
.
.
.
19. A video store charges a monthly membership fee of
$7.50, but the charge to rent each movie is only
$1.00 per movie. Another store has no membership
fee, but it costs $2.50 to rent each movie. How
many movies need to be rented each month for the
total fees to be the same from either company?
20. A professional cyclist is training for the Tour de
France. What was his average speed in miles per
hour if he rode the 120 miles from Laval to Blois in
4.7 hours? Use the formula
, and round your
answer to the nearest tenth.
21. The formula for the resistance of a conductor with
voltage V and current I is
. Solve for V.
22. Solve
23. To join the school swim team, swimmers must be
able to swim at least 500 yards without stopping.
Let n represent the number of yards a swimmer can
swim without stopping. Write an inequality
describing which values of n will result in a
swimmer making the team. Graph the solution.
for x.
24. Sam earned $450 during winter vacation. He needs to save $180 for a camping trip over spring break. He can
spend the remainder of the money on music. Write an inequality to show how much he can spend on music. Then,
graph the inequality.
25. Carlotta subscribes to the HotBurn music service.
She can download no more than 11 song files per
week. Carlotta has already downloaded 8 song files
this week. Write, solve, and graph an inequality to
show how many more songs Carlotta can
download.
26. Denise has $365 in her saving account. She wants
to save at least $635. Write and solve an inequality
to determine how much more money Denise must
save to reach her goal. Let d represent the amount
of money in dollars Denise must save to reach her
goal.
27. Marco’s Drama class is performing a play. He
wants to buy as many tickets as he can afford. If
tickets cost $2.50 each and he has $14.75 to spend,
how many tickets can he buy?
28. Solve the inequality z + 8  3z  –4 and graph the
solutions.
29. A family travels to Bryce Canyon for three days.
On the first day, they drove 150 miles. On the
second day, they drove 190 miles. What is the least
number of miles they drove on the third day if their
average number of miles per day was at least 180?
30. Mrs. Williams is deciding between two field trips
for her class. The Science Center charges $135 plus
$3 per student. The Dino Discovery Museum
simply charges $6 per student. For how many
students will the Science Center charge less than
the Dino Discovery Museum?
31. Fly with Us owns a D.C.10 airplane that has seats for 240 people. The company flies this airplane only if there are
at least 100 people on the plane. Write a compound inequality to show the possible number of people in a flight on
a D.C.10 with Fly with Us. Let n represent the possible number of people in the flight. Graph the solutions.
32. Tell whether the ordered pair (5, –3) is a solution of
the system
33. Solve the system
.
34. The Fun Guys game rental store charges an annual
fee of $5 plus $5.50 per game rented. The Game
Bank charges an annual fee of $17 plus $2.50 per
game. For how many game rentals will the cost be
the same at both stores? What is that cost?
by graphing.
35. If the pattern in the table continues, in what month will the number of sales of CDs and movie tickets be the same?
What number will that be?
Month
CDs
Movie tickets
Total Number Sold
1
2
700
685
100
145
3
670
190
4
655
235
36. Solve
by substitution. Express your
answer as an ordered pair.
37. Solve
by substitution. Express
your answer as an ordered pair.
38. Janice is going on vacation and needs to leave her
dog at a kennel. Nguyen’s Kennel charges $15 per
day plus $20 for a processing fee. The Pup Palace
Kennel charges $12 per day, and has a $35
processing fee. After how many days is the Pup
Palace Kennel cheaper than Nguyen’s Kennel?
39. Solve
by elimination. Express your
answer as an ordered pair.
40. Solve
by elimination. Express your
answer as an ordered pair.
41. Solve
by elimination. Express your
answer as an ordered pair.
42. At the local pet store, zebra fish cost $2.10 each
and neon tetras cost $1.85 each. If Marsha bought
13 fish for a total cost of $25.80, not including tax,
how many of each type of fish did she buy?
Algebra QBA 1 Review
Answer Section
SHORT ANSWER
1. ANS:
26 + n; 44 points
The expression 26 + n models the number of points Juan scored in all.
Evaluate 26 + n for n = 18.
26 + 18 = 44
If Juan scored 18 points in the second half of the game, then he scored 44 points in all.
PTS: 1
DIF: 2
OBJ: 1-1.4 Application
STA: MCC9-12.A.CED.1
TOP: 1-1 Variables and Expressions
DOK: DOK 3
2. ANS:
; 13 sand dollars
The expression
Evaluate
REF:
NAT:
LOC:
KEY:
0ef4d6a2-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.A.SSE.1
MTH.C.10.05.02.02.013 | MTH.C.10.05.02.02.019
algebraic expression | word problem | operation
models the number of sand dollars each of Salvador’s friends will receive.
for n = 10.
= 13
If Salvador gives 130 sand dollars to 10 friends, each friend will get 13 sand dollars.
PTS: 1
DIF: 2
REF: 0ef4fdb2-4683-11df-9c7d-001185f0d2ea
OBJ: 1-1.4 Application
NAT: NT.CCSS.MTH.10.9-12.A.SSE.1
STA: MCC9-12.A.SSE.1 | MCC9-12.A.CED.1
LOC: MTH.C.10.05.02.02.013 | MTH.C.10.05.02.02.019
TOP: 1-1 Variables and Expressions
KEY: algebraic expression | word problem | operation
DOK: DOK 3
3. ANS:
15y; 180 books
The expression 15y models the number books Isabel read in all.
Evaluate 15y for y = 12.
15(12) = 180
If Isabel read for 12 months, then that means Isabel read 180 books.
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 2
1-1.4 Application
MCC9-12.A.SSE.1a
1-1 Variables and Expressions
DOK 3
REF:
NAT:
LOC:
KEY:
0ef738fe-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.A.SSE.1
MTH.C.10.05.02.02.013 | MTH.C.10.05.02.02.019
algebraic expression | word problem | operation
4. ANS:
p = 22
Since 6 is subtracted from p, add 6 to both sides to undo the
subtraction.
Check:
To check your solution, substitute 22 for p in the original
equation.
PTS:
OBJ:
STA:
TOP:
DOK:
5. ANS:
s = 42
1
DIF: 1
REF: 0f88cffa-4683-11df-9c7d-001185f0d2ea
1-2.1 Solving Equations by Using Addition
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.004
1-2 Solving Equations by Adding or Subtracting
KEY: equation | solving | subtraction
DOK 2
Since 6 is added to s, subtract 6 from both sides to undo the addition.
Check:
To check your solution, substitute 42 for s in the original equation.
PTS: 1
DIF: 1
REF: 0f8b0b46-4683-11df-9c7d-001185f0d2ea
OBJ: 1-2.2 Solving Equations by Using Subtraction
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
STA: MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.005
TOP: 1-2 Solving Equations by Adding or Subtracting
KEY: equation | solving | addition
DOK: DOK 2
6. ANS:
s = 46
When something is added to the variable, add its opposite to both sides of the equation to isolate the variable. Here,
–14 is added to the variable, so add 14 to both sides of the equation to isolate s.
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 1
REF: 0f8d6da2-4683-11df-9c7d-001185f0d2ea
1-2.3 Solving Equations by Adding the Opposite
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.004
1-2 Solving Equations by Adding or Subtracting
KEY: equation | solving | subtraction
DOK 2
7. ANS:
The salaries for the second month are $11,689.
First month
Second month
Added
to
salaries
salaries
b
b + x = 21,894
10,205 + x = 21,894
–10,205
–10,205
+
x
is
21,894
=
21,894
Write an equation to represent the relationship.
Substitute 10,205 for b. Since 10,205 is added to x, subtract
10,205 from both sides to undo the addition.
The salaries for the second month are $11,689.
PTS:
OBJ:
NAT:
STA:
LOC:
TOP:
DOK:
8. ANS:
1
DIF: 2
REF: 0f8d94b2-4683-11df-9c7d-001185f0d2ea
1-2.4 Application
NT.CCSS.MTH.10.9-12.A.CED.1 | NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.CED.1 | MCC9-12.A.REI.3
MTH.C.10.06.01.009 | MTH.C.10.06.02.01.005
1-2 Solving Equations by Adding or Subtracting
KEY: equation | solving | addition | subtraction
DOK 3
The highest score is 56.
highest score
minus
h
–
lowest score
l
equals
=
score range
23
Write an equation to represent the relationship.
Substitute 33 for l.
Solve the equation.
PTS:
NAT:
STA:
LOC:
TOP:
DOK:
1
DIF: 3
REF: 0f8fcffe-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.A.CED.1 | NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.CED.1 | MCC9-12.A.REI.3
MTH.C.10.06.01.009 | MTH.C.10.06.02.01.004
1-2 Solving Equations by Adding or Subtracting
KEY: equation | solving | addition | subtraction
DOK 2
9. ANS:
q = 205
Since q is divided by 5, multiply both sides by 5 to undo the
division.
q = 205
Check:
To check your solution, substitute 205 for q in the original
equation.
PTS: 1
DIF: 1
REF: 0f92325a-4683-11df-9c7d-001185f0d2ea
OBJ: 1-3.1 Solving Equations by Using Multiplication
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
STA: MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.006
TOP: 1-3 Solving Equations by Multiplying or Dividing
KEY: equation | multiplication | solving
DOK: DOK 2
10. ANS:
n = 14
3n = 42
Since n is multiplied by 3, divide both sides by 3 to undo the
multiplication.
Check:
3n = 42
To check your solution, substitute 14 for n in the original equation.
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 1
REF: 0f92596a-4683-11df-9c7d-001185f0d2ea
1-3.2 Solving Equations by Using Division
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.007
1-3 Solving Equations by Multiplying or Dividing
KEY: equation | solving | multiplication
DOK 2
11. ANS:
The reciprocal of
is
multiply both sides by
. Since
is multiplied by
,
.
PTS: 1
DIF: 1
REF: 0f9494b6-4683-11df-9c7d-001185f0d2ea
OBJ: 1-3.3 Solving Equations That Contain Fractions
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
STA: MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.006
TOP: 1-3 Solving Equations by Multiplying or Dividing
DOK: DOK 2
12. ANS:
a = –15
First x is multiplied by –2. Then 14 is added.
Work backward: Subtract 14 from both sides.
Since x is multiplied by –2, divide both sides by –2 to undo the
multiplication.
PTS:
OBJ:
STA:
LOC:
TOP:
DOK:
13. ANS:
1
DIF: 1
REF: 0f99596e-4683-11df-9c7d-001185f0d2ea
3-1.1 Solving Two-Step Equations NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
MTH.C.10.06.02.01.005 | MTH.C.10.06.02.01.007 | MTH.C.10.06.02.01.008
3-1 Solving Two-Step and Multi-Step Equations
KEY: equation | two-step | multi-step
DOK 2
Since
is subtracted from
, add
to both sides to undo
the subtraction.
Since f is divided by 45, multiply both sides by 45 to undo the
division.
Simplify.
PTS:
OBJ:
NAT:
LOC:
TOP:
DOK:
1
DIF: 2
REF: 0f99807e-4683-11df-9c7d-001185f0d2ea
3-1.2 Solving Two-Step Equations That Contain Fractions
NT.CCSS.MTH.10.9-12.A.REI.3
STA: MCC9-12.A.REI.3
MTH.C.10.06.02.01.004 | MTH.C.10.06.02.01.006 | MTH.C.10.06.02.01.008
3-1 Solving Two-Step and Multi-Step Equations
KEY: equation | two-step | multi-step
DOK 2
14. ANS:
Use the Commutative Property of Addition.
Combine like terms.
Since 10 is added to 17a, subtract 10 from both sides to undo
the addition.
Since a is multiplied by 17, divide both sides by 17 to undo the
multiplication.
PTS: 1
DIF: 2
REF: 0f9bbbca-4683-11df-9c7d-001185f0d2ea
OBJ: 3-1.3 Simplifying Before Solving Equations
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
STA: MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.005 | MTH.C.10.06.02.01.007 | MTH.C.10.06.02.01.008
TOP: 3-1 Solving Two-Step and Multi-Step Equations
KEY: equation | two-step | multi-step
DOK: DOK 2
15. ANS:
13
After paying $24.95 for roller skates, the number of visits to the roller rink that Devon can afford is
.
PTS:
OBJ:
LOC:
KEY:
16. ANS:
1.55
1
DIF: 2
REF: 0f9e1e26-4683-11df-9c7d-001185f0d2ea
3-1.4 Problem-Solving Application
STA: MCC9-12.A.REI.3
MTH.C.10.06.02.01.008
TOP: 3-1 Solving Two-Step and Multi-Step Equations
multi-step | equation
DOK: DOK 2
Substitute 3750 for p, 3000 for n, and 900 for e.
Add 900 to both sides of the equation.
Divide both sides by 3000.
PTS:
NAT:
LOC:
KEY:
1
DIF: 3
NT.CCSS.MTH.10.9-12.A.CED.4
MTH.C.10.07.18.002
equation | two-step | multi-step
REF:
STA:
TOP:
DOK:
0fa08082-4683-11df-9c7d-001185f0d2ea
MCC9-12.A.CED.4
3-1 Solving Two-Step and Multi-Step Equations
DOK 3
17. ANS:
To collect the variable terms on one side, subtract 50q from both
sides.
Since 81 is subtracted from 2q, add 81 to both sides to undo the
subtraction.
Since q is multiplied by 2, divide both sides by 2 to undo the
multiplication.
PTS:
OBJ:
STA:
TOP:
DOK:
18. ANS:
1
n = 12
1
DIF: 2
REF: 0fa2e2de-4683-11df-9c7d-001185f0d2ea
3-2.1 Solving Equations with Variables on Both Sides
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.008 | MTH.C.10.06.02.01.009
3-2 Solving Equations with Variables on Both Sides
KEY: equation | two-step | multi-step
DOK 2
Combine like terms.
Add to undo the subtraction. Or subtract to undo the addition.
Then, divide to undo the multiplication.
1
n = 12
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 2
REF: 0fa309ee-4683-11df-9c7d-001185f0d2ea
3-2.2 Simplifying Each Side Before Solving Equations
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.05.02.02.018 | MTH.C.10.06.02.01.009
3-2 Solving Equations with Variables on Both Sides
KEY: equation | equivalent equation | terms
DOK 2
19. ANS:
5 movies
Let m represent the number of movies rented each month.
Here are the costs for each company (in dollars).
7.5 + m
=
2.5m
To collect the variable terms on one side, subtract m from both sides.
7.5 – m
=
2.5m – m
7.5
=
1.5 m
Divide both sides by 1.5.
=
m
5
=
m
PTS: 1
DIF: 2
REF: 0fa7a796-4683-11df-9c7d-001185f0d2ea
OBJ: 3-2.4 Application
STA: MCC9-12.A.REI.3
LOC: MTH.C.10.06.02.01.009
TOP: 3-2 Solving Equations with Variables on Both Sides
KEY: equation | solving | variables on both sides
DOK: DOK 2
20. ANS:
25.5 mph
Divide both sides by t.
Substitute the known values.
Simplify. Round to the nearest tenth.
PTS:
OBJ:
STA:
TOP:
DOK:
21. ANS:
V = Ir
1
DIF: 2
3-3.1 Application
MCC9-12.A.CED.4
3-3 Solving for a Variable
DOK 2
REF:
NAT:
LOC:
KEY:
0faa09f2-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.A.CED.4
MTH.C.10.07.18.002
solving for a variable | rate | speed | distance
Locate V in the equation.
Since V is divided by I, multiply both sides by I to undo the division.
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 1
REF: 0fac6c4e-4683-11df-9c7d-001185f0d2ea
3-3.2 Solving Formulas for a Variable
NAT: NT.CCSS.MTH.10.9-12.A.CED.4
MCC9-12.A.CED.4
LOC: MTH.C.10.07.18.002
3-3 Solving for a Variable
KEY: literal equation | solving | variables
DOK 2
22. ANS:
Add z to both sides.
Divide both sides by 4.
PTS:
OBJ:
TOP:
DOK:
23. ANS:
0
1
DIF: 1
REF: 0fac935e-4683-11df-9c7d-001185f0d2ea
3-3.3 Solving Literal Equations for a Variable
STA: MCC9-12.A.CED.4
3-3 Solving for a Variable
KEY: literal equation | solving for a variable
DOK 2
100 200 300 400 500 600 700 800 900 1000
n
The variable n must be greater than or equal to 500 yards for a swimmer to make the team. The graph should
include the number 500 (solid circle at 500) and all the numbers to the right of 500 on the number line.
PTS:
OBJ:
STA:
TOP:
DOK:
24. ANS:
1
DIF: 2
REF: 101318d2-4683-11df-9c7d-001185f0d2ea
4-1.4 Application
NAT: NT.CCSS.MTH.10.9-12.A.CED.1
MCC9-12.A.CED.3
LOC: MTH.C.10.08.02.01.005 | MTH.C.10.08.02.01.007
4-1 Graphing and Writing Inequalities
KEY: inequalities | graph | number line
DOK 2
;
s
–500
–400
–300
–200
–100
0
100
200
300
400
Sam has $450, but must save $180 of that for his camping trip.
If s is the amount he can spend on music, then
So,
500
.
.
s
–500
PTS:
NAT:
STA:
LOC:
KEY:
–400
–300
–200
–100
0
100
200
300
400
500
1
DIF: 3
REF: 1015541e-4683-11df-9c7d-001185f0d2ea
NT.CCSS.MTH.10.9-12.A.CED.1 | NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.CED.1 | MCC9-12.A.CED.3
MTH.C.10.08.02.01.005 | MTH.C.10.08.02.01.007
TOP: 4-1 Graphing and Writing Inequalities
inequalities | graph | number line
DOK: DOK 3
25. ANS:
s  3
0
1
2
3
4
5
6
7
8
9
number already downloaded
8
10
11
+
+
additional songs
s


weekly limit
11
Subtract 8 from both sides to undo the addition.
s

3
Since you can only download whole songs, graph the nonnegative integers less than or equal to 3.
0
1
PTS:
OBJ:
NAT:
STA:
TOP:
DOK:
26. ANS:
2
3
4
5
6
7
8
9
10
11
1
DIF: 2
REF: 1017dd8a-4683-11df-9c7d-001185f0d2ea
4-2.2 Problem-Solving Application
NT.CCSS.MTH.10.9-12.A.CED.1 | NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.N.Q.1
LOC: MTH.C.10.08.02.01.005 | MTH.C.10.08.02.01.007
4-2 Solving Inequalities by Adding or Subtracting
KEY: solving | inequality | word problem
DOK 2
;
Let d represent the amount of money in dollars Denise must save to reach her goal.
$365
plus
additional amount of money is at least
$635
in dollars
365
+
d
635
Since 365 is added to d, subtract 365 from both sides to undo the
addition.
365
365
Check the endpoint 270 and a number that is greater than the endpoint.
PTS:
OBJ:
NAT:
STA:
TOP:
KEY:
1
DIF: 2
REF: 101a18d6-4683-11df-9c7d-001185f0d2ea
4-2.3 Application
NT.CCSS.MTH.10.9-12.A.CED.1 | NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.CED.1 | MCC9-12.N.Q.1
LOC: MTH.C.10.08.02.01.01.003
4-2 Solving Inequalities by Adding or Subtracting
inequalities | solving | adding | subtracting
DOK: DOK 2
27. ANS:
5 tickets
Divide both sides by the ticket price. The inequality symbol does not
change.
Simplify.
5 is the largest whole number less than 5.9.
PTS:
OBJ:
LOC:
KEY:
28. ANS:
z  –3
1
DIF: 2
REF: 1023a246-4683-11df-9c7d-001185f0d2ea
4-3.3 Application
STA: MCC9-12.A.REI.3
MTH.C.10.08.02.01.01.005
TOP: 4-3 Solving Inequalities by Multiplying or Dividing
inequalities | solving | multiplying | dividing
DOK: DOK 2
–10 –8
–6
–4
–2
0
2
z + 8  3z  –4
4z + 8  –4
4z  –12
–6
–4
6
8
10
Combine like terms.
Subtract 8 from both sides.
Divide both sides by 4. When you divide by a negative number,
reverse the inequality symbol. When you divide by a positive
number, keep the same inequality symbol.
z  –3
–10 –8
4
–2
0
2
4
6
8
10

Use a solid circle when the value is included in the graph, such as with or  Use an empty circle when the value
is not included, such as with > or <.
PTS:
OBJ:
STA:
TOP:
DOK:
1
DIF: 2
REF: 102866fe-4683-11df-9c7d-001185f0d2ea
5-1.2 Simplifying Before Solving Inequalities
NAT: NT.CCSS.MTH.10.9-12.A.REI.3
MCC9-12.A.REI.3
LOC: MTH.C.10.08.02.01.01.007 | MTH.C.10.08.02.01.005
5-1 Solving Two-Step and Multi-Step Inequalities
KEY: multistep inequality | solving
DOK 2
29. ANS:
200 mi
Let d represent the distance the family drove on the third day. The average number of miles is the sum of the miles
of each day divided by 3.
( 150
plus
190
plus
d)
divided
3
is at
180
by
least
( 150
+
190
+
d)
÷
3
180
Since
is divided by 3, multiply both sides by 3
to undo the division.
Combine like terms.
Since 340 is added to d, subtract 340 from both sides to undo
the addition.
The least number of miles the family drove on the third day is 200.
PTS: 1
DIF: 2
REF:
OBJ: 5-1.3 Application
STA:
LOC: MTH.C.10.08.02.01.01.007
TOP:
KEY: inequalities | two-step | multi-step DOK:
30. ANS:
More than 45 students
Science
plus
$3
per
student
Center fee
$135
+
$3
s
102ac95a-4683-11df-9c7d-001185f0d2ea
MCC9-12.A.REI.3
5-1 Solving Two-Step and Multi-Step Inequalities
DOK 3
is less
than
<
$12
$6
per
student
s
135 + 3s < 6s
– 3s – 3s
135
< 3s
<
45 < s
If 45 < s, then s > 45. The Science Center charges less if there are more than 45 students.
PTS:
OBJ:
LOC:
KEY:
1
DIF: 2
REF: 102d2bb6-4683-11df-9c7d-001185f0d2ea
5-2.2 Application
STA: MCC9-12.A.REI.3 | MCC9-12.A.CED.1
MTH.C.10.08.02.01.01.007
TOP: 5-2 Solving Inequalities with Variables on Both Sides
multistep inequality | solving | word problem
DOK: DOK 3
31. ANS:
–250
–200
–150
–100
–50
0
50
100
150
200
Let n represent the possible number of people in the flight.
100
is less than or equal to
n
is less than or equal to
100
n
–250
–200
–150
–100
–50
0
50
100
150
250
240
240
200
250
PTS: 1
DIF: 2
REF: 103452ca-4683-11df-9c7d-001185f0d2ea
OBJ: 5-3.1 Application
NAT: NT.CCSS.MTH.10.9-12.A.CED.1
STA: MCC9-12.A.CED.1
LOC: MTH.C.10.08.02.01.006 | MTH.C.10.08.02.01.008
TOP: 5-3 Solving Compound Inequalities
KEY: inequalities | compound
DOK: DOK 2
32. ANS:
yes
Substitute 5 for x and –3 for y in both equations. Since these values make both equations true, (5, –3) is a solution
of the system.
PTS:
OBJ:
NAT:
STA:
TOP:
DOK:
1
DIF: 1
REF: 1120836e-4683-11df-9c7d-001185f0d2ea
6-1.1 Identifying Solutions of Systems
NT.CCSS.MTH.10.9-12.A.REI.6 | NT.CCSS.MTH.10.9-12.A.REI.11
MCC9-12.A.REI.6 | MCC9-12.A.REI.11
LOC: MTH.C.10.09.01.01.01.005
6-1 Solving Systems by Graphing KEY: ordered pair | system of equations | solution
DOK 2
33. ANS:
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
–4
–6
–8
–10
Write each equation in slope-intercept form,
. Plot the y-intercept (0, b), and use the slope (m) to find a
second point on the line. Draw the second line in the same way. Find the coordinates of the point where the lines
intersect. This is the solution.
PTS:
OBJ:
NAT:
STA:
TOP:
DOK:
1
DIF: 2
REF: 1122beba-4683-11df-9c7d-001185f0d2ea
6-1.2 Solving a System of Linear Equations by Graphing
NT.CCSS.MTH.10.9-12.A.REI.6 | NT.CCSS.MTH.10.9-12.A.REI.11
MCC9-12.A.REI.6 | MCC9-12.A.REI.11
LOC: MTH.C.10.09.01.01.01.005
6-1 Solving Systems by Graphing KEY: coordinate plane | graphing | solving | system of equations
DOK 2
34. ANS:
4 games; $27
Write a system of equations.
Fun Guys
Game Bank
Total cost
y
y
is
=
=
cost
5.5
2.5
per game
plus
+
+
annual fee
5
17
Graph the two equations.
100
y
90
80
70
60
50
40
30
20
10
3
6
9
12
15
18
21
x
The lines appear to intersect at (4, 27). So the cost will be the same after 4 games, and that cost will be $27.
PTS: 1
DIF: 2
REF: 11252116-4683-11df-9c7d-001185f0d2ea
OBJ: 6-1.3 Problem-Solving Application
STA: MCC9-12.A.REI.6 | MCC9-12.A.REI.11
LOC: MTH.C.10.09.01.01.01.004
TOP: 6-1 Solving Systems by Graphing
KEY: systems of linear equations | solving systems of linear equations | two unknowns
DOK: DOK 2
35. ANS:
Month 11; 550
Continue the pattern. Subtract 15 from the number of CDs and add 45 to the number of movie tickets. In month 11,
both the number of CDs and the number of movie tickets will be 550.
PTS:
STA:
LOC:
TOP:
DOK:
1
DIF: 3
REF: 11254826-4683-11df-9c7d-001185f0d2ea
MCC9-12.A.REI.6 | MCC9-12.A.REI.11
MTH.C.10.09.01.01.01.002 | MTH.C.10.09.01.01.01.003
6-1 Solving Systems by Graphing KEY: pattern | arithmetic
DOK 3
36. ANS:
(2, 3)
Step 1
The second equation is solved for y.
Step 2
Substitute
for y in the first equation.
Simplify and solve for x.
Step 3
Divide both sides by 4.
x = 2
Step 4
y = 2
3
Write one of the original equations.
Substitute 2 for x.
Find the value of y.
(2, 3)
Write the solution as an ordered pair.
PTS: 1
DIF: 1
REF: 11278372-4683-11df-9c7d-001185f0d2ea
OBJ: 6-2.1 Solving a System of Linear Equations by Substitution
NAT: NT.CCSS.MTH.10.9-12.A.REI.6
STA: MCC9-12.A.REI.6
LOC: MTH.C.10.09.01.01.01.001
TOP: 6-2 Solving Systems by Substitution
KEY: system of equations | substitution
DOK: DOK 2
37. ANS:
(4, 8)
x = 2y – 12
Solve the second equation for x.
Step 1
Step 2
4(2y – 12) – 4y = –16
Substitute 2y – 12 for x in the first equation.
Step 3
8y – 48 – 4y = –16
4y – 48 = –16
4y = –16 – (48)
4y = 32
y=8
Use the Distributive Property to simplify.
Collect like terms.
Subtract 48 from both sides.
Divide both sides by 4.
Step 4
x – 2y = –12
x – 2(8) = –12
x – 16 = –12
x = –12 – (–16)
x=4
Write one of the original equations.
Substitute 8 for y.
(4, 8)
Write the solution as an ordered pair.
Step 5
Subtract –16 from both sides.
PTS: 1
DIF: 2
REF: 1129e5ce-4683-11df-9c7d-001185f0d2ea
OBJ: 6-2.2 Using the Distributive Property
NAT:
NT.CCSS.MTH.10.9-12.A.REI.6
STA: MCC9-12.A.REI.6
LOC: MTH.C.10.02.03.002 | MTH.C.10.09.01.01.01.001
TOP: 6-2 Solving Systems by Substitution
KEY: system of equations | substitution
DOK: DOK 2
38. ANS:
The Pup Palace Kennel is cheaper than Nguyen’s Kennel after 5 days.
Let t represent the total amount paid and let d represent the number of days.
Nguyen’s Kennel:
Pup Palace:
Substitute
for t in the second equation and solve for w.
The costs for the two kennels are equal at 5 days. After that, the Pup Palace Kennel is cheaper.
PTS: 1
DIF: 2
REF: 112a0cde-4683-11df-9c7d-001185f0d2ea
OBJ: 6-2.3 Application
STA: MCC9-12.A.REI.6
LOC: MTH.C.10.09.01.01.01.001
TOP: 6-2 Solving Systems by Substitution
KEY: system of equations | substitution
DOK: DOK 2
39. ANS:
(4, –1)
Step 1 2x – 3y = 11
3x + 3y = 9
The y-terms have opposite coefficients.
5x = 20
Add the equations to eliminate the y terms.
x=4
Step 2
PTS:
OBJ:
STA:
TOP:
KEY:
DOK:
2(4) – 3y = 11
8 – 3y = 11
– 3y = 3
y = –1
Substitute for x in one of the original equations.
Simplify and solve for y.
(4, –1)
Write the solution as an ordered pair.
1
DIF: 1
REF: 112eaa86-4683-11df-9c7d-001185f0d2ea
6-3.1 Elimination Using Addition NAT: NT.CCSS.MTH.10.9-12.A.REI.6
MCC9-12.A.REI.6
LOC: MTH.C.10.09.01.01.01.002
6-3 Solving Systems by Elimination
linear equation | system of equations | solving | elimination
DOK 2
40. ANS:
(–5, –8)
Multiply all expressions in the second equation by
.
Add the two equations together.
Divide both sides by 2.
Solve for x.
Substitute the value for x into one of the original equations and
solve for y.
PTS: 1
DIF: 2
REF: 112ed196-4683-11df-9c7d-001185f0d2ea
OBJ: 6-3.2 Elimination Using Subtraction
NAT: NT.CCSS.MTH.10.9-12.A.REI.6
STA: MCC9-12.A.REI.6
LOC: MTH.C.10.09.01.01.01.003
TOP: 6-3 Solving Systems by Elimination
KEY: system of equations | elimination
DOK: DOK 2
41. ANS:
(4, 3)
First, multiply each equation by a number to get opposite coefficients.
Multiply the first equation by –3
and the second by 5 to get opposite
y-coefficients.
Step 1
Add the two equations to eliminate the y-term.
Step 2
Simplify and solve for x.
x=4
Write one of the original equations.
Substitute 4 for x. Simplify and solve for y.
Step 3
y=3
PTS:
OBJ:
STA:
KEY:
1
DIF: 2
REF: 11310ce2-4683-11df-9c7d-001185f0d2ea
6-3.3 Elimination Using Multiplication First NAT:
NT.CCSS.MTH.10.9-12.A.REI.6
MCC9-12.A.REI.6
TOP: 6-3 Solving Systems by Elimination
system of equations | elimination
DOK: DOK 2
42. ANS:
7 zebra fish, 6 neon tetras
Let z be the number of zebra fish and let n be the number of neon tetras that Marsha bought. Then solve the
following system of equations.
Marsha spent $25.80.
Marsha bought 13 fish.
Multiply the second equation by –2.10
Add the two equations to eliminate the z term.
Solve for n.
To solve for z, substitute 6 for n in the first equation.
Simplify.
Solve for z.
PTS:
OBJ:
TOP:
DOK:
1
DIF: 2
REF: 11336f3e-4683-11df-9c7d-001185f0d2ea
6-3.4 Application
STA: MCC9-12.A.REI.6
6-3 Solving Systems by Elimination
KEY: system of equations | elimination
DOK 2