Solve each equation.
1. –8.8z = –17.6
a. –8.8
b. –26.4
Solve:
Check:
Solve each equation.
1. –8.8z = –17.6
ANSWER: c
c. 2
d. 8.8
_________________
2. –27.09 = 3.87a
a. –7
2. –27.09 = 3.87a
ANSWER: a
b. –23.22
c. 7
d. 30.96
_________________
3.
b = –2
3. 1/6 b = -2
ANSWER: a
a. –12
b. 4
c.
d. –8
________________
x=
4.
4. 1/80 x = 1/10
ANSWER: a
a. 8
b. 800
c. 4
d. 16
_________________
5. 11 = 3 + 4x
a.8
b.
c. 2
d. 32
5. 11 = 3 + 4x
ANSWER: c
6. y + 15 = 4
a. 7
6 b.
c. –44
Solve:
Check:
6. ¼ y + 15 =4
ANSWER: c
d.
7. Terrell is saving to
buy a video game
system that costs
$187.25. He paid a
deposit of $50.75
and will save an
additional $19.50 per
week to pay for the
system. Solve 50.75
+ 19.50w = 187.25 to
find the number of
weeks Terrell will
need to save money
for the video game
system.
7. ANSWER: a
a. 7 weeks
b. 12 weeks
c. 8 weeks
d. 6 weeks
______________
8. Melanie is reading a
book that has 335
pages. She has
already read 111 pages
of the book and will
read an additional 16
pages per night. Solve
111 + 16n = 335 to find
how many more nights
it will take Melanie to
finish the book.
8. ANSWER: d
Translate each sentence into an equation. Then find each number.
9. Two less than the product of a number and –5 is –42.
a.
b.
c.
d.
ANSWER: c
10. The sum of eleven and seven times a number is –17.
a.
b.
c.
d.
ANSWER: a
11. The difference of nine, and a number divided
by four is 13.
a.
b.
c.
d.
ANSWER: c
12. The difference of a number divided by five and twelve is –1.
a.
b.
c.
d.
ANSWER: a
13. Seven times a number plus the sum of three and twice
a number is 30.
a.
b.
c.
d.
ANSWER: d
Solve each problem by writing and solving an equation.
14. For his son’s birthday party, Mr. Mori bought four equally-priced pizzas and a $3 bag of
potato chips. If he spent$39, find the cost of each pizza.
a.
b.
c.
d.
ANSWER: c
15. Julian’s pool currently has twelve inches of water in it. He can pump eight inches of water
into the pool every hour. In how many hours will the pool have 60 inches of water in it?
a.
b.
c.
d.
ANSWER: b
16. Isabel and Ruth scored a total of twenty-two points in their last basketball game. Ruth
scored two more points than Isabel. How many points did Isabel score?
a.
b.
c.
d.
ANSWER: c
17. –116.6 = –22(p + 3)
a. 8.3
b. 2.3
c. –2.3
d. 5.44
ANSWER: b
Write the inequality for the graph.
18.
a.
b.
c.
d.
ANSWER: a
19.
b
.
a. t≤0
b.
c.
c
.
d.
ANSWER: b
d
.
A
N
S
W
E
R
:
b
a
.
b
.
c
.
d
.
A
N
S
W
E
MATH TEST
Equations
Grade 6 Math Advanced
Castro - 201
Name:
Date: _________________________
Part 1: Multiple Choice
(Bubble the correct answer in pencil only!)
Teacher Score:
Part 1:
______
Part 2:
______
Part 3:
______
Total:
______
Grade:
______
SHOW ALL WORK FOR CREDIT! Please write neatly, so that I can understand your
work. Use a pencil, and if you make a mistake erase it completely. Do not scribble
on your test paper.
20. Alex, Eve, Edward, and Nicole participated in a relay race competition. The table
below shows the distance traveled by each of them in the race.
Name
Distance (mi)
Alex
?
Eve
17
Edward
?
Nicole
2
0
All of them covered a total distance of 152 miles. If Edward ran twice the distance
that both Alex and Eve ran, find the distance covered by Alex and Edward.
Alex, Eve, Edward, and Nicole participated in a relay race competition. The table below shows the distance
traveled by each of them in the race.
Name
Distance (mi)
?
17
?
2
Alex
Eve
Edward
Nicole
All of them covered a total distance of 152 miles. If Edward ran twice the distance that both Alex and Eve ran,
find the distance covered by Alex and Edward.
ANSWER: Distance covered by Alex is 33 miles.
Distance covered by Edward is 100 miles.
2(a+17) +a+17+2=152
2a+34+a+17+2=152
3a+53=152
3a=99
A=33
2(33+17)
2(50) = 100
The table below shows the sales of two different ice cream flavors on a Saturday.
Flavor
Vanilla
Strawberry
Units
Sold4
2
0
5
21. If the number of units of vanilla ice cream sold Sunday is at least 20 more than the
number sold Saturday, write an inequality for the number of units of vanilla ice cream
sold Sunday. Then graph the solution on a number line.
The table below shows the sales of two different ice cream flavors on a Saturday.
Flavor
Vanilla
Strawberry
Units Sold
40
25
If the number of units of vanilla ice cream sold Sunday is at least 20 more than the number sold Saturday, write
an inequality for the number of units of vanilla ice cream sold Sunday. Then graph the solution on a number line.
ANSWER:
22. There are three different types of earthquakes. A deep earthquake has a magnitude
of at least 6. Suppose a shallow earthquake has a magnitude of 3. Write and solve an
inequality to find how much the magnitude can increase so the earthquake is a deep
earthquake.
b. A deep earthquake has a magnitude of 7. Write and solve an inequality to find how
much magnitude must decrease so that the earthquake is downgraded to a shallow
earthquake of at least magnitude 3.
Answer: There are three different types of earthquakes.
a. A deep earthquake has a magnitude of at least 6. Suppose a shallow earthquake has a magnitude of 3. Write
and solve an inequality to find how much the magnitude can increase so the earthquake is a deep earthquake.
b. A deep earthquake has a magnitude of 7. Write and solve an inequality to find how much magnitude must
decrease so that the earthquake is downgraded to a shallow earthquake of at least magnitude 3.
ANSWER: a.
b.
at least 3
at least 4
23. Lucy has 4 times as many balls as Charles. Charles has 4 fewer balls than Cindy.
Suppose a bag has 13 balls. If Lucy, Charles, and Cindy together have 4 times as many
balls as are in the bag, then find the number of balls each of them has.
Lucy has 4 times as many balls as Charles. Charles has 4 fewer balls than Cindy. Suppose a bag has 13 balls. If
Lucy, Charles, and Cindy together have 4 times as many balls as are in the bag, then find the number of balls
each of them has.
ANSWER: Cindy—12
Charles—8
Lucy—32
C+ c-4 +4(c-4) =52
C+c-4+4c-16=52
6c-20=52
6c=72
C=12
C-4=8
4(8) = 32