Raider Day 1
Percentage Word Problems
Teacher: Pat Puckett
Contact Info: 270-786-4958 (home)
Text via Remind 101 or email at
[email protected]
ACT Standard AF 301. Solve routine one-step
Available 9:00 am – 6:00 pm
arithmetic problems using positive rational numbers, such
as single-step percent
KYOTE Standard 3 Perform arithmetic calculations involving fractions, decimals, and percents.
Notes and Examples:
When reading a word problem that involves percentages, you need to first make sure you
understand the question that is being asked. If a percentage is given in the problem, you will
need to convert the percent to a decimal by dividing the percent by 100. In word problems,
there are some common words that appear quite often. “Is” means equals and “of” means times.
One of the easiest ways to solve percentage problems is to set them up as an equation. See the
examples below:
Example 1: A baseball pitcher won 80% of the games he pitched. If he pitched 35 ballgames,
how many games did he win?
a) First, what is the question asking? 80% of 35 is what?
b) Now, set up the equation to solve. Change 80% to a decimal by moving the decimal
point to the left two places or dividing by 100.
80% of 35 is what?
.80 * 35 = x
Multiply 35 by .80
28 = x
So the pitcher won 28 games
Example 2: Jerry, an electrician, worked 7 months out of the year. What percent of the
year did he work? (Round answer to the nearest hundredth)
a) There are 12 months in 1 year.
b) What is the question asking?
c) The equation would be
What percent of 12 is 7?
x
* 12 = 7
x = .5833 ≈58.33%
Example 3: Percent of Increase and Decrease
To find the percent of increase or decrease, use the following formula:
difference of the original and new amount
original amount
Divide both sides by
12 to solve
Multiply decimal by
100 to get the
percent
A large screen TV that originally sells for $900 is marked down to $684. What is the
percentage of decrease in the price?
a) First find the reduction in cost by subtracting the new cost from the original cost.
900  684  116
b) Next divide the reduction in cost (116) by the original cost of the TV (900).
116
 0.24
900
c) Change the decimal to a percent by moving the decimal two places to the right or
multiplying the decimal by 100. So, the percent of decrease is 24%.
Example 4: Tom, Dick, and Harry are friends who go shopping. Tom buys a shirt for $25.
Dick buys a shirt for 15% more than Tom’s shirt, and Harry buys a shirt for 20% more than
Dick’s shirt. What was the combined cost of all three shirts?
a) Tom paid $25
b) Dick’s cost is 15% more than Tom’s, so find out what 15% of 25 would be by multiplying
0.15  25  3.75 . Add this number to Tom’s cost 25  3.75  28.75 So, Dick paid $28.75
for his shirt.
c) Harry paid 20% more than Dick, so 28.75  0.20  5.75 Now add the 5.75 to Dick’s cost
of his shirt 5.75  28.75  34.50 Harry paid $34.50 for his shirt.
d) Add all of the costs together to get the combined total 25  28.75  34.50  88.25 The
total cost was $88.25.
Answer the following questions:
1) In a word problem, the word is generally means _______________________.
2) In a word problem, the word of generally means _______________________.
3) To change a percent to a decimal, you must ______________________________.
4) To change a decimal to a percent, you must _______________________________.
5) What is the formula for percent of increase/decrease? ________________________.
6) What question(s) do you still have after reading these notes and examples?
_______________________________________________________________________
Percent Word Problems.
Directions: Choose 10 of the following problems to solve. Set up a basic percent
problem. Show the equation and how to solve the problem. Follow rounding directions.
Answers with no supporting work will only receive half credit.
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 hundredth.)
4) A woman put $580 into a savings account for one year. The rate of interest on the
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account was 6 % . How much was the interest for the year in dollars and cents? (Round
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to the nearest cent.)
5) A student answered 86 problems on a test correctly and received a grade of 98%. If all
the problems on the test were worth the same number of points, how many problems
were on the test? (Round to the nearest whole number.)
6) Manuel found a wrecked Ford F-150 truck that he could fix. He bought the truck for
65% of the original price of $11,200. What did he pay for the truck? (Round to the
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.)
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8) A work crew is made of 8 men and the rest are women. If 66 % of the work crew are
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men, how many people are on the work crew?
9) A sports store near Big Bear Lake is having a 20% off sale on all water skis. What will the
sale price be for water skis which regularly sell for $248?
10) Skis at a sports store near Snow Summit are on sale for $476. If the original price was
$560, what discount rate does this represent?
11) The average fine for entering a National Forest Wilderness without a permit increased
from $65 to $78. What rate of increase is this?
12) A stereo is marked down $75. If this is a 15% decrease, find the sale price?
13) A stereo system is marked down from $450 to $382.50. What is the discount rate?
14) Rosa received a monthly raise of $162.50. If this represented a 6.5% increase, what is
her monthly salary after the raise?
15) Yahoo in Sunnyville currently has a staff of 6200 employees. Next month, Yahoo will
decrease its staff by 8%. How many people will be employed by Yahoo next month?
16) A managers’ salary at Green Dot increased from $48,000 to $51,360. What is the rate
of increase?