1. Practice Quiz Word Problems
Friday, September 14, 2018Friday, September 14, 2018

2. 0 < 2n – 2 < 100 2 < 2n < 102 2 2n 102 < 2
For how many integer values of n is it true that 2n – 2 is an integer greater than 0 and less than 100? 1
0 < 2n – 2 < 100 +2 +2 +2
Integers between
1 and 51
2 < 2n < 102 n 2
<
51 – 1 = 50
50 – 1 = 49
1 < n < 51

3. If the sum of two integers x and k is less than x, which of the following must be true?2
x + k < x –x –x
k < 0

4. Twice the square of certain integer is 3 less than 7 times the integer.
Which of the following equations
represents the statement above? 3
2N2 = 7N – 3
2N2 – 3 = 7N
2N2 = 3 – 7N

5. Which of the following equations represents the statement above? 4
Twice the difference between a certain number and its square root is 15 more than twice the number.
Which of the following equations represents the statement above? 4

6. If a number is doubled and then increased by 10, the result is 5 less than the square of the number.
Which of the following equations represents the statement above? 5
2N + 10 = N2 – 5
2N + 10 = N2 + 5

7. A. a – b = 4 a = 2b + 1 B. b – a = 4 a = 2b + 1 C. a – b = 4
If a > b, then the difference between a and b is 4. The number a is 1 more than twice the number b. Which of the following pairs of equations could be used to find a and b? 6
A. a – b = 4
a = 2b + 1
B. b – a = 4
a = 2b + 1
C. a – b = 4
b = 2a + 1
D. b – a = 4
b = 2a + 1
E. b – a = 4
2b = a + 1

8. A. p + q = 24 q = p2 – 1 B. p + q = 24 p2 + 1 = q C. p + q = 24
The product of p and q is 24. q is one less than the square of p.
Which of the following pairs of equations could be used to find p and q? 7
A. p + q = 24
q = p2 – 1
B. p + q = 24
p2 + 1 = q
C. p + q = 24
q2 = p – 1
D. pq = 24
q = p2 – 1
E. pq = 24
p = q2 – 1

9. Let 1st number = x Let 2nd number = x + 2 2(x + 2) = 17 + x
There are two consecutive odd integers such
that twice the greater is 17 more than the lesser. Find the larger number. 8
Let 1st number = x
Let 2nd number = x + 2
2(x + 2) = 17 + x
Larger Number
= x + 2 =
= 15
2x + 4 = x –x –x
x + 4 = 17 –4 –4
x = 13

10. x – 2 3(x – 2) 3(x – 2) = x + 6 2x – 6 = 6 3x – 6 = x + 6 +6 +6 –x –x
If 2 is subtracted from a number and this difference is tripled, the result is 6 more than the number. Find the number. 9
Let number = x
‘2 is subtracted from a number’ =
x – 2
3(x – 2)
‘The difference is tripled’ =
3(x – 2) = x + 6
2x – 6 = 6
3x – 6 = x + 6 +6 +6 –x –x
2x = 12
2x – 6 =
x = 6

11. Larry books Judy books x 2x – 3 5 2(5) – 3 10 – 3 7
Judy has 3 less than twice the number of books that Larry has. If Larry has 5 books,
how many books does Judy have? 10
Larry books
Judy books x
2x – 3 5
2(5) – 3
10 – 3 7

12. ‘number is increased by 8’ = k + 8 ‘The result is doubled’ = 2(k + 8)
A certain number k is increased by 8, and the result is then doubled. The new result is 8 less than 3 times the original number, k.
What is the value of k ? 11
Let number = k
‘number is increased by 8’ =
k + 8
‘The result is doubled’ =
2(k + 8)
2(k + 8) = 3k – 8
16 = k – 8
2k = 3k – 8 +8 +8
–2k
–2k
24 = k
16 = k – 8

13. Let 1st integer = x 19 Let 2nd integer = x + 1 19+1 = 20
If the sum of three consecutive integers equals 60, what is the greatest of the integers? 12
Method #1
Let 1st integer = x 19
Let 2nd integer = x + 1
19+1 = 20
Let 3rd integer = x + 2
19+2 = 21
x + x x + 2 = 60
3x = 60 –3 –3
3x = 57
x = 19

14. If the sum of three consecutive integers equals 60, what is the greatest of the integers?12
Method #2
Test each answer, assuming it is the greatest integer.
Greatest
Middle
Smallest
Sum
A. 18
B. 19
C. 20
D. 21
E. 22 18 17 16 51 NO 19 18 17 54 NO 20 19 18 57 NO 21 20 19 60
YES

15. Let 1st integer = x 13 Let 2nd integer = x + 2 13+2 = 15
If the sum of two consecutive odd integers is 28, what is the product? 13
Let 1st integer = x 13
Let 2nd integer = x + 2
13+2 = 15
x + x + 2 = 28
Sum =
= 28
2x = 28 –2 –2
2x = 26
Product
= 13  15
= 195
x = 13

16. –15 3 –5 –2 Let integer = x 2x + 10 = x2 – 5 –2x – 10 –2x – 10
If a positive integer is doubled and then increased by 10, the result is 5 less than the square of the integer. What is the integer? 14
Let integer = x
2x = x2 – 5
–15
–2x – 10
–2x – 10 3 –5
0 = x2 – 2x – 15 –2
0 = (x + 3)(x – 5)
Two numbers with
Product of –15 and
Sum of –2
x + 3 = 0 ,
x – 5 = 0
x = –3
x = 5

17. Cost of pencil = A Cost of pen = B Jon  1A + 2B = 3.50 Lauren 
Jon buys one pencil and two pens for $ Lauren buys four pencils and three pens for $ How much would one pencil and one pen cost? 15
Cost of pencil = A
Cost of pen = B
Jon 
1A + 2B = 3.50
(Multiply Jon by –4)
Lauren 
4A + 3B = 5.50
Jon 
–4A – 8B = –14.00
Add
Equations
Lauren 
4A + 3B =
– 5B = –8.50
B =
(Pen cost)

18. the original equations. 1A + 2B = 3.50 1A + 2B = 3.50 4A + 3B = 5.50
Jon buys one pencil and two pens for $ Lauren buys four pencils and three pens for $ How much would one pencil and one pen cost? 15
Cost of pencil = A
Cost of pen = B
B = 1.70 (Pen cost)
Find A. Use one of
the original equations.
1A + 2B = 3.50
1A + 2B = 3.50
4A + 3B = 5.50
A + 2(1.70) = 3.50
Cost of pencil and pen
= A B
= = 1.80
A = 3.50
A = 0.10

19. Cost of sandwich = S Cost of juice = J #1  S + J = 3.60 S + J = 3.60
Penny bought a sandwich and a container of juice for $ The sandwich costs three times as much as the juice. How much did the sandwich cost? 16
Cost of sandwich = S
Cost of juice = J
Substitute S = 3J
into #1
#1 
S + J = 3.60
S + J = 3.60
#2 
S = 3J
3J + J = 3.60
4J = 3.60
(Juice cost)
J = 0.90

20. (Juice cost) Cost of sandwich = S J = 0.90 Cost of juice = J #1 
Penny bought a sandwich and a container of juice for $ The sandwich costs three times as much as the juice. How much did the sandwich cost? 16
(Juice cost)
Cost of sandwich = S
J = 0.90
Cost of juice = J
Find S by
letting J = 0.90
#1 
S + J = 3.60
#2 
S = 3J
S = 3J
S = 3(0.90)
(Sandwich cost)
S = 2.70

21. Wendy designed a billboard 6 feet high and 12 feet wide
Wendy designed a billboard 6 feet high and 12 feet wide. Eric has designed a billboard with the same area that is 8 feet high. How wide is Eric’s billboard? 17
Note: Both billboards have the same area.
Inverse
Variation
6 · 12 = 8 · W2
x1y1 = x2y2
Eric’s
Width
9 feet
72 = 8W2
9 = W2
Eric’s length increased, but Eric’s width decreased.

22. If y varies directly as x2, and y = 3 when
x = 3, what is the value of y when x is 6? 18
y varies directly as x
y varies directly as x2

23. If y2 varies directly as 2x, and y = 4 when x = 1, what is the value of y when x = 4?19
y varies directly as x
y2 varies directly as 2x

24. There are about 200 calories in 50 grams of Swiss cheese
There are about 200 calories in 50 grams of Swiss cheese. Willie ate 70 grams of this cheese. About how many calories were in the cheese that he ate if the number of calories varies directly as the weight of the cheese. 20

25. A salesman's commission varies directly as his sales
A salesman's commission varies directly as his sales. Write the formula relating this situation and denote the variables. If the commission is $100 for $1000 in sales, find the commission
for $1750 in sales. 21

26. 5  p = 2  100 5p = 200 p = 40 22 Direct Variation
Students receive 5 bonus points for every 2 community service projects they perform. If Mark received 100 bonus points, how many projects did he perform? 22
Note: As the bonus points increase, the community service projects should increase.
Direct
Variation
5  p = 2  100
5p = 200
p = 40

27. If it takes 4 men 3 hours each to pave a playground, how many hours will it take
12 men to complete the same task? 23
Note: Increasing the number of men will decrease
the amount of time to complete the task.
Inverse
Variation
M1H1 = M2H2
4 · 3 = 12 · H2
x1y1 = x2y2
12 = 12H2
1 Hour
1 = H2

28. 24
Assume “W varies inversely as R”. 
If W is 200 when R=4, find W when R=10. 

29. In kick boxing, it is found that the force, f, needed to break a board, varies inversely with the length, l, of the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 6 feet long? 25