Math Word Problems n e w y o r k

a. 30 inches
b. 215.9 inches
c. 33.5 inches
d. 47.2 inches
50.
A bag contains 3 red, 6 blue, 5 purple, and 2 orange marbles. One marble
is selected at random. What is the probability that the marble chosen is
blue?
a.

1
4
3

b.
3
8
c.

1
3
6

d.
3
5
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501 Math Word Problems
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1 1
51.
The operator of an amusement park game kept track of how many tries it
took participants to win the game. The following is the data from the first
ten people:
2, 6, 3, 4, 6, 2, 8, 4, 3, 5
What is the median number of tries it took these participants to win the
game?
a. 8
b. 6
c. 4
d. 2
52.
Max goes to the gym every fourth day. Ellen’s exercise routine is to go
every third day. Today is Monday and both Max and Ellen are at the gym.
What will the day of the week be the next time they are BOTH at the
gym?
a. Sunday
b. Wednesday
c. Friday
d. Saturday
53.
Danny is a contestant on a TV game show. If he gets a question right, the
points for that question are added to his score. If he gets a question wrong,
the points for that question are subtracted from his score. Danny currently
has 200 points. If he gets a 300-point question wrong, what will his score
be?
a.
−100
b. 0
c.
−200
d. 100
54.
Write 3.5 
× 10
4
in decimal notation.
a. 3.50000
b. 35,000
c. 350,000
d. 0.00035
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55.
The Ravens played 25 home games this year. They had 9 losses and 2 ties.
How many games did they win?
a. 14
b. 11
c. 13
d. 12
56.
The temperature at midnight was 4°F. By 2 
A
.
M
. it had dropped 9°F. What
was the temperature at 2 
A
.
M
.?
a. 13°F
b.
−5°F
c.
−4°F
d. 0°F
57.
Find the next number in the following pattern.
320, 160, 80, 40, . . . 
a. 35
b. 30
c. 10
d. 20
58.
Which of the following terms does NOT describe the number 9?
a. prime
b. integer
c. real number
d. whole number
59.
Which expression below is equal to 5?
a. (1 + 2)
2
b. 9 
− 2
2
c. 11 
− 10 × 5
d. 45 ÷ 3 
× 3
60.
A bus picks up a group of tourists at a hotel. The sightseeing bus travels 2
blocks north, 2 blocks east, 1 block south, 2 blocks east, and 1 block south.
Where is the bus in relation to the hotel?
a. 2 blocks north
b. 1 block west
c. 3 blocks south
d. 4 blocks east
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1 3
61.
Each week Jaime saves $25. How long will it take her to save $350?
a. 12 weeks
b. 14 weeks
c. 16 weeks
d. 18 weeks
62.
Ashley’s car insurance costs her $115 per month. How much does it cost
her per year?
a. $1,150
b. $1,380
c. $980
d. $1,055
63.
The ratio of boys to girls at the dance was 3:4. There were 60 girls at the
dance. How many boys were at the dance?
a. 45
b. 50
c. 55
d. 40
501 Math Word Problems
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Answer Explanations
1.
d. Work backwards to find the solution. George has 5 cousins, which is 11
less than Bonnie has; therefore, Bonnie has 16 cousins. Bonnie has twice
as many as Robert has, so half of 16 is 8. Robert has 8 cousins.
2.
c. Set up a proportion with 

m
sod
il
a
k

; 
2
5
= 
1
x
0

. Cross multiply and solve; (5)(10) =
2x. Divide both sides by 2; 
5
2
0

= 
2
2
x

; x = 25 sodas.
3.
b. To earn an average of 93% on four tests, the sum of those four tests
must be (93)(4) or 372. The sum of the first three tests is 85 + 92 + 95 =
272. The difference between the needed sum of four tests and the sum
of the first three tests is 100. He needs a 100 to earn a 93 average.
4.
c. To find the number of boxes needed, you should divide the number of
cans by 40; 320 ÷ 40 = 8 boxes.
5.
d. From 10 
A
.
M
. Friday to 10 
A
.
M
. Saturday is 24 hours. Then, from 10
A
.
M
. Saturday to 6 
P
.
M
. Saturday is another 8 hours. Together, that
makes 32 hours.
6.
b. Use the order of operations and try each option. The first option results
in 14 because 2 
× 5 = 10, then 10 + 4 = 14. This does not work. The
second option does result in 18. The numbers in parentheses are added
first and result in 9, which is then multiplied by 2 to get a final answer
of 18. Choice c does not work because the operation in parentheses is
done first, yielding 6, which is then multiplied by 5 to get a result of 30.
Choice d does not work because the multiplication is done first, yielding
8, which is added to 5 for a final answer of 13.
7.
a. Multiply the number of miles (9) by the amount pledged per mile
($0.50); 9 
× 0.50 = $4.50. To multiply decimals, multiply normally, then
count the number of decimal places in the problem and place the
decimal point in the answer so that the answer has the same number of
decimal places as the problem.
8.
d. To find the square root (
) you ask yourself, “What number
multiplied by itself gives me 36?” 6 
× 6 = 36; therefore, 6 is the square
root of 36.
9.
c. Mr. Brown plows 6 acres an hour, so divide the number of acres (21) by
6 to find the number of hours needed; 21 ÷ 6 = 3.5 hours.
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1 5
10.
d. This is the only answer choice that has only PRIME numbers. A prime
number is a number with two and only two distinct factors. In choice a,
42 is not prime. In choice b, 4 and 6 are not prime. In choice c, 6 is not
prime.
11.
c. 2
5
= 2 
× 2 × 2 × 2 × 2 = 32
12.
b. Visualize a number line. The distance from 
−4 to 0 is 4. Then, the
distance from 0 to 63 is 63. Add the two distances together to get 67; 
63 + 4 = 67.
13.
d. Exceeded means “gone above.” Therefore, if they exceeded their goal of
$9,500 by $2,100, they went over their goal by $2,100; $9,500 + $2,100
= $11,600. If you chose a, you subtracted $2,100 from $9,500 instead of
adding the two numbers.
14.
a. Subtract Mt. Kilimanjaro’s height from Mt. Everest’s height; 29,028 
−
19,340 = 9,688. If you chose b, you did not borrow correctly when
subtracting.
15.
a. To find the area of a square, you multiply the length of a side by itself,
because all the sides are the same length. What number multiplied by
itself is 64? 8 
× 8 = 64.
16.
b. Subtract the number of students present from the total number in the
class to determine how many students are missing; 26 
− 21 = 5.
17.
c. Divide the money raised by three to find the amount each charity will
receive; $1,569 ÷ 3 = $523.
18.
d. Find the number of points scored on two-point baskets by multiplying 2
× 10; 20 points were scored on two-point baskets. Find the number of
points scored on three point baskets by multiplying 3 
× 2; 6 points were
scored on three-point baskets. The total number of points is the sum of
these two totals; 20 + 6 = 26.
19.
a. From 2:15 
P
.
M
. to 4:15 
P
.
M
. is 2 hours. Then, from 4:15 
P
.
M
. to 4:45 
P
.
M
.
is another half hour. This is a total of 2.5 hours.
20.
b. There is a 1 in 6 chance of rolling a 5 because there are 6 possible
outcomes on a die, but only 1 outcome is a 5.
21.
a. Find the rate at which Susan is traveling by dividing her distance by
time; 114 ÷ 2 = 57 mph. To find out how long it will take her to travel
285 miles, divide her distance by her rate; 285 ÷ 57 = 5 hours.
501 Math Word Problems
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22.
d. Divide the miles by the time to find the rate; 3,060 ÷ 5 = 612 mph.
23.
c. He spent $72 on pants (3 
× $24 = $72) and $90 on shirts (5 × $18 = $90).
Altogether he spent $162 ($72 + $90 = $162). If you chose a, you
calculated the cost of ONE pair of pants plus ONE shirt instead of
THREE pants and FIVE shirts.
24.
b. There are 100 cm in a meter. A square meter is 100 cm by 100 cm. The
area of this is 10,000 sq cm (100 
× 100 = 10,000).
25.
a. There are 36 inches in a yard; 4 
× 36 = 144 inches. There are 144 inches
in 4 yards.
26.
c. To find the number of hours needed to burn 750 calories, divide 750 by
500; 750 ÷ 500 = 1.5 hours.
27.
b. Visualize a number line. The drop from 31° to 0° is 31°. There are still
9 more degrees to drop. They will be below zero. 
−9°F is the
temperature at midnight.
28.
a. Divide the total sales ($1,260) by the number of tickets sold (210) to
find the cost per ticket; $1,260 ÷ 210 = $6.
29.
c. A 10 second count is 
1
6
of a minute. To find the number of beats per
minute, multiply the beat in 10 seconds by 6; 11 
× 6 = 66 beats per
minute.
30.
c. The probability of heads does not change based on the results of
previous flips. Each flip is an independent event. Therefore, the
probability of getting heads is 
1
2
.
31.
b. To find the median, first put the numbers in order from least to greatest.
56, 72, 87, 89, 93. The middle number is the median. 87 is in the
middle of the list, therefore, it is the median. If you chose a, you forgot
to put the numbers in order before finding the middle number.
32.
a. List the factors of 24 and 64. The largest factor that they have in
common is the greatest common factor.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 64: 1, 2, 4, 8, 16, 32, 64
The largest number that appears in both lists is 8.
33.
d. Find the total number of slices by multiplying 3 by 8 (3 
× 8 = 24). There
are 24 slices to be shared among 12 coworkers. Divide the number of
slices by the number of people to find the number of slices per person;
24 ÷ 12 = 2 slices per person.
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1 7
34.
a. Divide the number of people by the number that fit on a bus; 125 ÷ 48 =
2.604. They need more than 2 buses, but not quite 3. Since you can’t
order part of a bus, they will need to order 3 buses.
35.
d. Change all the answer choices to their decimal equivalents. Choice a is
still 0.6; choice b is 0.6; choice c is 0.6 (3 ÷ 5); choice d is 0.06; 0.06 is
not equivalent to the other numbers.
36.
b. Lance has 70 cents. Three-fourths of a dollar is 75 cents, so Margaret
has 75 cents. Guy has 60 cents (25 + 25 + 10 = 60). Bill has 60 cents 
(6 
× 10 = 60). Margaret has the most money.
37.
b. Finding what 100 students would say is the same as finding the percent,
because percent means “out of 100.” To find the percent, divide the
number of students who said a dog was their favorite (258) by the total
number of students surveyed (430); 258 ÷ 430 = 0.6. Change 0.6 to a
percent by moving the decimal two places to the right. 60%. This
means that 60 out of 100 students would say dog.
38.
c. Divide the bill by 5; $53.75 ÷ 5 = $10.75. They each pay $10.75.
39.
d. Find how much it depreciates over one year by dividing the cost by 5;
$2,100 ÷ 5 = $420. Multiply this by 2 for two years; $420 
× 2 = $840. It
will have depreciated $840.
40.
b. Add the test grades (96 + 74 + 85 = 255) and divide the sum by the
number of tests (255 ÷ 3 = 85). The average is 85%.
41.
b. Find the total number of people and the total number of cars. Then,
divide the total people by the total cars.
People:
57 
× 4 =
228
61 
× 2 =
122
9 
× 1 = 
9
5 
× 5 = 
25
TOTAL
384 people
Cars:
57 + 61 + 9 + 5 = 132
384 ÷ 132 = 2.9 which is rounded up to 3 people because 2.9 is closer to
3 than it is to 2.
42.
c. Find the number of gallons per second by dividing 750 by 50 (750 ÷ 50
= 15 gallons per second). Divide 330 gallons by 15 to find how many
seconds it will take (330 ÷ 15 = 22 seconds). It will take 22 seconds.
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43.
c. Divide 405 by 45 to get 9 minutes.
44.
c. Find the probability of each event separately, and then multiply the
answers. The probability of rolling a 3 is 
1
6
and the probability of tossing
a tail is 
1
2
. To find the probability of both of them happening, multiply 
1
6
×
1
2
= 

1
1
2

. The probability is 

1
1
2

.
45.
c. Multiply the number of choices for each item to find the number of
combinations (5 
× 8 = 40). There are 40 combinations.
46.
c. There are 12 inches in a foot. Divide 150 by 12 to find the number of
feet; 150 ÷ 12 = 12.5 feet.
47.
a. One cup is 8 ounces, so half a cup is 4 ounces. Multiply 25 by 4 ounces
to find the number of ounces needed; 25 
× 4 = 100 ounces.
48.
c. There are 16 ounces in a pound. If Justin gains 8 ounces he will be 8
pounds and 20 ounces. The 20 ounces is 1 pound and 4 ounces. Add this
to the 8 pounds to get 9 pounds and 4 ounces.
49.
c. Divide the width (85 cm) by 2.54 to find the number of inches; 85 ÷
2.54 = 33.46 inches. The question says to round to the nearest tenth
(one decimal place), which would be 33.5 inches.
50.
b. The probability of blue is 

t
b
o
l
t
u
a
e
l

. The number of blue marbles is 6, and the
total number of marbles is 16 (3 + 6 + 5 + 2 = 16). Therefore, the
probability of choosing a blue is 

1
6
6

= 
3
8
.
51.
c. First, put the numbers in order from least to greatest, and then find the
middle of the set.
2, 2, 3, 3, 4, 4, 5, 6, 6
The middle is the average (mean) of the 5th and 6th data items. The
mean of 4 and 4 is 4.
52.
d. A chart like the one below can be used to determine which days Max
and Ellen go to the gym. The first day after Monday that they both
go—Saturday—is the answer.
today
next day they 
are both at 
the gym
 S 
M  Tu  W 
Th 
F 
S
 
 M,E  
  E  M
 E 
 
M 
E 
 
  M,E
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1 9
53.
a. 200 
− 300 = −100 points
54.
b. Move the decimal point 4 places to the right to get 35,000.
55.
a. Eleven games are accounted for with the losses and ties (9 + 2 = 11).
The remainder of the 25 games were won. Subtract to find the games
won; 25 
− 11 = 14 games won.
56.
b. If the temperature is only 4° and drops 9°, it goes below zero. It drops
4° to zero and another 5° to 
−5°F.
57.
d. Each number is divided by 2 to find the next number; 40 ÷ 2 = 20.
Twenty is the next number.
58.
a. Nine is NOT prime because it has 3 factors; 1, 3, and 9. Prime numbers
have only 2 factors.
59.
b. The correct order of operations must be used here. PEMDAS tells you
that you should do the operations in the following order:
Parentheses, Exponents, Multiplication and Division—left to right,
Addition and Subtraction—left to right.
9 
− 2
2
= 9 
− 4 = 5
a is (1 + 2)
2
= (3)
2
= 9
c is 11 
− 10 × 5 = 11 − 50 = − 39
d is 45 ÷ 3 
× 3 = 15 × 3 = 45
5
°
4
°
3
°
2
°
1
°
0
°
−1°
−2°
−3°
−4°
−5°
−6°
501 Math Word Problems
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60.
d. See the diagram below. They are 4 blocks east of the hotel.
61.
b. Divide $350 by $25; 350 ÷ 25 = 14 weeks.
62.
b. Multiply $115 by 12 because there are 12 months in a year; 
$115 
× 12 = $1,380 per year.
63.
a. Use a proportion comparing boys to girls at the dance.

g
b
i
o
r
y
l
s
s

3
4
= 

6
x
0

Solve the proportion by cross-multiplying, setting the cross-products
equal to each other and solving as shown below.
(3)(60) = 4x
180 = 4x

18
4
0

= 
4
4
x

45 = x
There were 45 boys.

Hotel
4 blocks east
End

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In order to 
understand arithmetic in general, it is important to practice
and become comfortable with fractions and how they work. The problems
in this chapter help you practice how to perform basic operations with
fractions and will assist you in understanding their real-world applications.
64.
Lori ran 5
1
2
miles Monday, 6
1
4
miles Tuesday, 4
1
2
miles Wednesday,
and 2
3
4
miles on Thursday. What is the average number of miles
Lori ran?
a. 5
b. 4
1
2
c. 4
d. 4
3
4
65.
Last year Jonathan was 60
3
4
inches tall. This year he is 65
1
4
inches
tall. How many inches did he grow?
a. 5
1
2
b. 4
1
2
c. 4
1
4
d. 5
3
4
2
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66.
Larry spends 
3
4
hour twice a day walking and playing with his dog. He also
spends 
1
6
hour twice a day feeding his dog. How much time does Larry
spend on his dog each day?
a.
1
1
1
2

hour
b. 1
1
2
hours
c. 1
5
6
hours
d. 1
2
5
hours
67.
The first section of a newspaper has 16 pages. Advertisements take up 3
3
8
of the pages. How many pages are not advertisements?
a. 12
5
8
b. 19
3
8
c. 13
d. 12
1
2
68.
Lisa was assigned 64 pages to read for English class. She has finished 
3
4
of
the assignment. How many more pages must she read?
a. 48
b. 21
c. 16
d. 8
69.
Mark has three 4
1
2
oz cans of tomatoes and five 8
1
4
oz cans. How many
ounces of tomatoes does Mark have?
a. 12
3
4
b. 54
3
4
c. 54
d. 62
1
4
70.
Joe walked 2
1
2
miles to school, 
1
3
mile to work, and 1
1
4
miles to his friend’s
house. How many miles did Joe walk altogether?
a. 3
1
9
b. 4

1
1
2

c. 4
1
9
d. 4
2 2
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2 3
71.
Justin read 
1
8
of a book the first day, 
1
3
the second day, and 
1
4
the third day.
On the fourth day he finished the book. What part of the book did Justin
read on the fourth day?
a.
2
5
b.
3
8
c.

2
7
4

d.
1
2
7
4

72.
Tammi babysat for 4
1
2
hours. She charged $7 an hour. How much should
she get paid?
a. $28.50
b. $35
c. $28
d. $31.50
73.
The painting crew has 54
2
3
miles of center lines to paint on the highway. If
they have completed 23
1
5
miles, how many miles do they have to go?
a. 31

1
7
5

b. 31
1
1
3
5

c. 21

1
4
5

d. 31
1
2
74.
Which of the fractions below is greater than 1
1
2
?
a.
7
5
b.
3
2
1
0