Section 3 – 3 !
Applied Number Problems
Selected Worked Homework Problems
1. Ann Marie sold 6 more Cell Phones than Larry . If they sold a total of 80 phones then how many
did each of them sell?
Larry is mentioned second so
Larry = x
Ann Marie = x + 6
!
Ann Marie sold 6 more cell phones than the number Larry sold (x)
x + x + 6 = 80 (thei total cell phones sold was 80)
2x +6 = 80
2x = 74
x = 37
x = 37 and x + 6 = 43
Larry sold 37 cell phones and Ann Marie sold 43 cell phones.
2. Susan works 15 more hours at her day job than her night job. If she works a total of 71 hours,
how many hours does she work at each of her jobs?
Night Job is mentioned second so
night job = x
Day job = x + 15
!
15 more hours at her day job than her night job.(x)
x + x + 15 = 71 (t works a total of 71 hours)
2x + 15 = 71
2x = 56
x = 28
x = 28 and x + 15 = 43
Sandra works 28 hours at her night job and 43 hours at the day job.
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
4. Tom has budgeted his monthly expenses. He will spend $ 120 more for food than he does for
gas. He will spend six times the amount for rent as he will for gas. How much should he budget
for each of them if he has a total of $ 520 a month to spend on these items?
Gas is mentioned second so
gas = x
Food = x + 120
Rent = 6x
120 more for food than for gas. (x)
rent is six times the amount he spends or gas (x)
!
x + x + 120 + 6x = 520 (their total is 520)
8x + 120 = 520
8x = 400
x = 50
x = 50 and x + 120 = 170 and 6x = 300
Tom spends $ 50 on Rent, $170 on Food and $300 on rent
9. A Toyota Prius can travel 3 more than twice as many miles on a given amount of gas as a Toyota
Camry. A Toyota Highlander travels 15 miles less on the same amount of gas as a Toyota Camry.
If all three cars travel a total of 116 miles on the same amount of gas, how far did each car travel?
Camry is mentioned second so
Camry = x
Prius = 2x + 3
3 more than twice as many miles as a Toyota Camry.(x)
Highlander = x – 15
!
15 miles less on the same amount of gas as a Toyota Camry (x)
x + 2x + 3 + x – 15 = 116 (their total is 116)
4x – 12 = 116
4x = 128
x = 32
x = 32 and 2x + 3 = 67 and x – 15 = 17
The Camry traveled 32 miles , the Prius traveled 67 miles and the Highlander traveled 17 miles
page 8
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
11. Eppieʼs Great Race happens each Spring by the Sacramento River. There are 3 legs to the race.
The second leg of the race is 9 miles longer than the first leg. The third leg of the race is 14
miles longer than the first leg. If the total for the three legs of the race is 59 miles, how long are
the three legs of the race?
The first leg is mentioned second so First leg = x
!
Second leg = x + 9
9 miles longer than the first leg. (x)
Third leg = x + 14
14 miles longer than the first leg (x)
x + x + 9 + x + 14 = 59
(the total is 59)
3x + 23 = 59
3x = 36
x = 12
x = 12 and x + 9 = 21 and x + 14 = 26
The first leg is 12 miles long, the second leg is 21 miles long and the third part is 26 miles long.
12. Ann Marie, Tom and David earn 130 dollars checking answers for a math book. Ann Marie
earns twice as much as Tom. David earns 10 dollars less than Ann Marie. How much does
each one of them make?
NOTE: Davis is 10 less that Ann Marie no 10 less than Tom
Tom is mentioned second so Tom = x
Ann Marie = 2x
twice as much as Tom (x)
David = 2x – 10
!
10 less than Ann Marie (WHO IS 2x)
x + 2x + 2x – 10 = 130
(the total is 130)
5x – 10 = 130
5x = 140
x = 28
x = 28 and 2x = 56 and 2x – 10 = 46
Tom makes 28 dollars , Ann Marie makes 56 dollars and David makes 46 dollars
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
13. Find the sides of a rectangle if the length is 2 more than three times the width. The perimeter of
the rectangle is 52 inches.
The width is mentioned second so Width = x
Length = 3x + 2
2 more than three times the width. (x)
Length = 3x + 2
Width = x
Length = 3x + 2
Width = x
Width = x
Length = 3x + 2
The perimeter (x + x + 3x + 2+3x+2) is equal to 52
8x + 4 = 52
8x = 48
x=6
and
3x + 2 = 3(6) + 2 = 20
The width is 6 inches and the length is 20 inches
14. Find the sides of a rectangle if the length is 12 less than three times the width. The perimeter of
the rectangle is 112 inches.
The width is mentioned second so Width = x
Length = 3x – 12
2 less than four times the width (x)
Length = 3x – 12
Width = x
Length = 3x – 12
Width = x
Width = x
Length = 3x – 12
!
!
!
!
The perimeter (x + x + 3x − 12 + 3x − 12) is equal to 112
8x − 24 = 112
8x = 136
x = 17
and
3x − 12 = 3(17) − 12 = 39
The width is 17 inches and the length is 39 inches
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
15. Find the 3 sides of a triangle if the second side is 10 more than the first side. The third side is
4 less than 2 times the first side. The perimeter is 54 yards.
S1 is mentioned second so S1 = x
S2 = x + 10
S3 = 2x – 4
10 more than the first side (x)
4 less than 2 times the first side (x)
The perimeter (x+x+10 + 2x − 4) is equal to 54
4x + 6 = 54
4x = 48
x = 12
and
S1 = 12
S2 = 12 + 10 = 22
S3 = 2 •12 − 4 = 20
S1 is 12 yd. , S2 is 22 yd. and S3 is 20 yd.
!
17. Find the 3 sides of a triangle if the second side is 10 more than the first side. The third side
is 5 more than the SECOND SIDE. The perimeter is 70 cm.
S1 is mentioned second so S1 = x
S2 = x + 10
10 more than the first side (x)
S3 = x + 10 + 5 5 more than the SECOND SIDE. WHICH is x + 10
The perimeter (x + x +10 + x + 10 + 5) is equal to 70
3x + 25 = 70
3x = 45
x = 15
and
S1 = 7
S2 = 7 + 8 = 15
S3 = 7 + 8 − 5 = 10
S1 is 7 ft. , S2 is 2 5 ft.and S3 is 30 ft.
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
Complementary Angles: 2 angles whose total is 90 degrees
Supplementary Angles : 2 angles whose total is 180 degrees
21. Find two complementary angles if the second angle is 12 less than the first angle.
∠1 is mentioned second so ∠1= x
∠ 2 = x -–12
12 less than the first angle (x)
The total of the 2 angles (x + 2x − 12) is equal to 90
3x − 12 = 90
2x = 102
x = 34
and
∠1 = 34
∠2 = 2 i 34 − 12 = 56
∠1 is 34 degrees and ∠ 2 is 56degrees
23. The sum of three angles is 152 degrees. Angle A is 18 degrees less than Angle B. Angle C is
30 degrees less than twice as large as Angle B. Find the measure of all 3 angles.
∠ B is mentioned second so ∠ B = x
∠ A = x – 18
∠ C = 2x – 30
18 degrees less than ∠ B (x)
30 degrees less than twice as large as ∠ B (x)
The total of the 3 angles (x + x − 18 + 2x − 30) is equal to 152
4 x − 48 = 152
4 x = 200
x = 50
and
∠ B = 50
∠A = 50 − 18 = 32
∠C = 2 • 50 − 30 = 70
∠ B is 50 degrees , ∠ A is 32 degrees
Math 100 !
and ∠ C is 70 degrees
Section 3–3 HW WKD !
© 2016 Eitel
25. Sue has 8 more dimes than he has nickels. She has $ 2.60 total. Find how many of each type
of coin she has.
Let the number of nickels = x
Let the number of dimes = x + 8
(8 more dimes than nickels)
⎛number of 1⎞⎛ value of 1 coin of ⎞ ⎛ number of the other⎞⎛ value of 1 coin of ⎞
⎜
⎟⎜
⎟+ ⎜
⎟⎜
⎟ = total of all coins
that type
type of coin ⎠⎝ that type
⎝type of coin⎠⎝
⎠ ⎝
⎠
!
nickels!
!
x(.05)
!
dimes !
+ (x + 8)(.10) = 2.60
x(5) + (x + 3)(10) = 260
(multiply each term by 100 to eliminate the decimals)
! 5x + 10x +80 = 260
distribute the 10
! 15x + 80 = 260
15x = 180
!
!
!
x = 12 (the number of nickels)
and the number of dimes = x + 8 =12 + 8 = 30
answer: The number of nickels is 12 and the number of dimes is 20
!
Math 100 !
Check: 12(.05) + 20(.10) = 2.60
Section 3–3 HW WKD !
© 2016 Eitel
27. Bill has 5 more than twice as many dimes as he has quarters. He has a total of $ 9.50. Find
how many of each type of coin Bill has.
Let the number of quarters = x
Let the number of dimes = 2x + 5
(5 more than twice as many quarters)
⎛number of 1⎞⎛ value of 1 coin of ⎞ ⎛ number of the other⎞⎛ value of 1 coin of ⎞
⎜
⎟⎜
⎟+ ⎜
⎟⎜
⎟ = total of all coins
that type
type of coin ⎠⎝ that type
⎝type of coin⎠⎝
⎠ ⎝
⎠
!
!
!
quarters !
!
x (.25)
+
dimes!
(2x + 5) (.10) = 9.50
x(25) + (2x + 5)(10) = 950
(multiply each term by 100 to eliminate decimals)
x(25) + (2x + 5)(10) = 950
distribute the 25
! 25x + 20x + 50 = 950
! 45x + 50 = 950
! 45x = 900
!
x = 20 (the number of quarters)
!
and the number of dimes = 2x + 5 = 2(20) + 5 = 45
!
Answer: The number of quarters is 20 and the number of dimes is 45
!
Check: 20(.25) + 45(.10) = 5.00 + 4.50 = $ 9.50
Math 100 !
Section 3–3 HW WKD !
© 2016 Eitel
29. Joe has 4 less than twice as many quarters as half dollars. He has 2 less dimes than quarters.
Find how many of each type of coins he has if the value of the coins total $ 10.40.
The number of half dollars = x
The number of quarters = 2x – 4
(4 less than twice as many half dollars)
The number of dimes = 2x – 4 – 2
( 2 less dimes than quarters)and quarters are 2x – 4
⎛ number of ⎞ ⎛ value of 1 ⎞ ⎛ number of ⎞ ⎛ value of 1⎞ ⎛ number of ⎞ ⎛ value of ⎞
⎜⎝ half dollars⎟⎠ ⎜⎝ half dollar ⎟⎠ + ⎜⎝ quarters ⎟⎠ ⎜⎝ quarter ⎟⎠ + ⎜⎝ dimes
⎟⎠ ⎜⎝ 1 dime ⎟⎠ = total of all coins
half
dollars
quarters !
!
dimes!
x (.50)
+ (2x – 4) (.25)
+ (2x – 4 – 2) (.10) = 10.40
x (.50)
+ (2x – 4) (.25)
+ (2x – 6 ) (.10) = 10.40
(add like terms for the number of dimes
x (50) + (2x – 4) (25) + (2x – 6 (10) = 1040 (multiply each term by 100 to eliminate decimals)
x (50) + (2x – 4) (25) + (2x – 6 (10) = 1040
distribute the 25 and the 10
50x + 50x – 100 + 20x – 60= 1040
120x - 160= 1040
120x = 1200
x = 10 (the number of half dollars)
the number of quarters = 2x – 4 = 2(10) – 4 = 16
the number of dimes = 2x – 4 – 2 = 2(10) – 6 = 14
Answer: The number of half dollars is 10.
The number of quarters is 16 and the number of dimes is 14
!
Math 100 !
Check: 10(.50) + 16(.25) + 14(.10) = 5.00 + 4.50 = $ 10.60
Section 3–3 HW WKD !
© 2016 Eitel
30. The Folsom College bookstore sells used books at $ 30 and new books at $ 50 They plan to
sell 4 times as many used books as new books and take in $17,000. How many books of each
type do they need to sell?
the number of new books = x
the number of used books = 4x
(4 times as many used books as new books)
⎛ number of ⎞ ⎛ value of 1
⎜⎝ new books ⎟⎠ ⎜⎝ new book
⎞ ⎛ number of ⎞ ⎛ value of 1 ⎞
⎟⎠ + ⎜⎝ used books⎟⎠ ⎜⎝ new book ⎟⎠ = total cost
!
!
new book
!
x (50)
!
used book
+
(4x) (30) = 17,000
50x + 120x + = 17,000
!
170 x = 17,000
!
!
x = 100 new books
and the used books = 4( 100) = 400
!
Answer:
!
The number new books is 100 and the number of used books is 400
!
Math 100 !
Check: 100(50) + 400(30) = 5,000 + 12,000 = $17,000
Section 3–3 HW WKD !
© 2016 Eitel