Percent Word Problems
Ratio and proportion method
Here are several
aids that will help you solve word problems:
1.
Make sure you understand the question that is asked
2.
Sort out the information to make a basic percent
problem, such as “30% of what is 17?”
3.
Sometimes, you will have to subtract
or add some of the numbers.
4.
The base will
always be the original number, price, or total.
Some examples of percent word problems.
A baseball pitcher won 80% of the games he pitched. If he pitched 35 ballgames, how many games did he win?
80% of 35 is what?
80 =
100 35
1.
Multiply the opposites
80 x 35 = 2800
2. Divide by the remaining
number
28
Jerry, an electrician, worked 7 months out of the year.
What percent of the year
did he work? (round
answer to the nearest hundredth)
What percent
of 12 is 7? 12 months = 1 year
1.
Multiply the opposites
= 7
100 12
7 x 100 =
700
2. Divide by the remaining
number
58.33
12 700.00
58.33% (rounded to
hundredth)
Sometimes the information needed to solve a percent
word problem is not stated directly.
You will need to sort out the
numbers given in the problem. Organizing all the information into a box format will help you see what numbers you have and what you need.
Some examples.
There are 28 students in a class. Sixteen of those students are men. What percent of the class are women? (Round to the nearest tenth)
|
Men
|
%
|
16
|
|
Women
|
%
|
12
|
|
Total
|
100%
|
28
|
|
|
28 total students
-16 men 12 women
12 is what % of 28?
= 12
1. Multiple the opposites
100 x 12 = 1200
2.
Divide by
the remaining number
100 28
`
42.85
28 1200.00
42.9%
Donovan took a math test and got 35 correct and 10 incorrect answers. What was the percentage of correct answers?
(Round to the nearest hundredth)
|
Correct answers
|
%
|
35
|
|
Incorrect answers
|
%
|
10
|
|
Total answers
|
100%
|
45
|
|
|
35 correct answers
+10 incorrect answers
45 total answers
35 is what %
of 45?
= 35
100 45
1. Multiple the opposites
100 x 35 = 3500
2.
Divide by the remaining
number
77.777
45 3500.000
77.78
% (rounded to hundredth)
Percent Word Problems
Directions: Set up a basic percent problem.
Sometimes you will have to do extra steps to solve the problem. Follow rounding directions. Answers and solutions start on page 6.
1)
A student earned
a grade of 80% on a math test that had
20 problems. How many problems
on this test did the student answer correctly? (round to the nearest whole number)
2)
There are 36 carpenters in a crew. On a certain day, 29 were present.
What percent showed
up for work? (round to the nearest
tenth)
3)
A metal bar weighs
8.15 ounces. 93% of the bar is silver. How many ounces of silver are in the bar? (round to the nearest thousandth)
4)
A woman put $580 into a savings
account for one year. The rate of interest
on the account
was 6½%. How much was the interest
for the year in dollars and cents? (Round to the nearest cent)
5)
A student answered
86 problems on a test correctly and received
a grade 98%. How many problems were on the test, if all the problems
were worth the same number of points? (Round to the nearest whole number)
6)
Manuel found a wrecked Trans-Am that he could fix. He bought the car for 65% of the original price of $7200. What did he pay for the car? (Round to nearest dollar)
7)
Pamela bought an electric
drill at 85% of the regular price.
She paid $32.89
for the drill. What was the regular
price? (Round
to the nearest
cent)
8)
A crew is made
up of 8 men; the rest are women.
66 2 % of
3
the crew are men. How many people
are in the crew?
9)
Ben earns $12,800 a year. About 15% is taken out for taxes. How much is taken out for taxes?
10)
At a sale, shirts were sold for $15 each. This price was 80% of their original
price. What was the original
price?
11)
There are 32 students
in a class. Nine of those students
are women. What percent are men? (round
to the nearest tenth)
12)
The Royals
softball team played 75 games and won 55 of them. What percent
of the games did they lose? (round to the nearest
tenth)
Answer Key
1. 80 = Multiply
the opposites:
100 20
80 x 20 = 1600
Divide by the remaining number:
16
100 1600
2.
100
= 29
36
Multiply the opposites:
29 x 100 = 2900
Divide by the remaining number:
80.55
3. 93 = Multiply
the opposites:
100
8.15
93 x 8.15
= 757.95
Divide by the remaining number:
7.5795
100
7.580 ounces
757.9500
4. =
580
Multiply
the opposites:
6 ½ x 580 = 3770
Divide by the remaining number:
37.70
5. 98 = 86
100
Multiply the opposites:
100 x 86 =
8600
Divide by the remaining number:
87.7
98 8600.0
88 problems (rounded to nearest whole)
6. 65 = Multiply
the opposites:
100
7200
65 x 7200 =
468,000
Divide by the remaining number:
4680
7. 85 = 32.89
100
Multiply the opposites:
100 x 32.89
= 3289
Divide by the remaining number:
38.694
85 3289.000
8. = 8
100
$38.69
Multiply
the opposites:
100 x 8 = 800
Divide by the remaining number:
4
800 ¸ 66
2
= 800 ¸ 200
= 800 ´ 3
= 12
15 Multiply the opposites:
9. =
100
12,800
15 x 12,800 = 192,000
Divide by the remaining number:
1920
100 192000
10.
80 = 15
100
Multiply the opposites:
100 x 15 =
1500
Divide by the remaining number:
18.75
80 1500.00
|
Total
|
100%
|
32
|
|
Men
|
|
23
|
|
Women
|
|
9
|
|
|
11.
100
= 23
32
$18.75
32
- 9
23
Multiply the opposites:
100 x 23 =
2300
Divide by the remaining number:
71.87
32 2300.00
71.9%(rounded
to nearest tenth)
|
Total
|
100%
|
75
|
|
Won
|
|
55
|
|
Lost
|
|
20
|
|
|
12.
100
= 20
75
75
- 55
20
Multiply
the opposites:
100 x 20 = 2000
Divide by the remaining number:
26.667
75 2000.000
26.7% games lost (rounded
to tenth)
