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Math problems involving percents can
be tricky. They can be worded in many
different ways, and getting set up to
solve them is confusing.
These questions appear on standardized
tests very frequently. The foolproof key
to success with percent problems is to
rewrite the question as an equation!
To write an equation, you must TRANSLATE
from an English sentence into an equation
(a mathematical sentence).
Here’s how…
When you see the word “what,”
replace it with a variable like
x because that is the unknown part we
are looking for.
When you see the word “is,”
replace it with a “equals”
sign.
When you see the word “of,”
replace it with
multiplication.
When you see a percent,
replace it with its decimal
form.
When you see…
Replace it with…
“What”
a variable (x) because this is
the unknown part that we
are trying to find
“Is”
=
“Of”
multiplication
a percent
its decimal form
Example 1:
40 is 12 percent of what number?
STEP 1: TRANSLATE / REPLACE
Go on to the next page to continue.
Example 1:
40 is 12 percent of what number?
STEP 1: TRANSLATE / REPLACE
40 =
.12
˚
(x)
Go on to the next page to continue.
Example 1:
40 is 12 percent of what number?
STEP 1: TRANSLATE / REPLACE
40 =
.12
˚
STEP 2: SOLVE
(x)
(divide both sides by .12)
Go on to the next page to continue.
Example 1:
40 is 12 percent of what number?
STEP 1: TRANSLATE / REPLACE
40 =
.12
˚
STEP 2: SOLVE
(x)
(divide both sides by .12)
x = 333.3
STEP 3: CHECK THAT YOUR
ANSWER IS REASONABLE
Example 2:
What is 15% of 350?
Example 2:
What is 15% of 350?
x
= .15
˚ 350
Solve (multiply .15 by 350): x = 52.5
Example 3:
What percent of 75 is 20?
Example 3:
What percent of 75 is 20?
x%
˚ 75=20
Solve (divide both sides by 75): x = 0.26
Since our final answer should be a PERCENT here, we
need to convert from decimal form to percent form.
Final answer: 26. 6%
Practice: Write an equation for each, then solve.
1.
What is 45 percent of 300?
2.
What percent of 20 is 8?
3.
64 is what percent of 800?
4.
12 percent of what number is 90?
5. 40 percent of 85 is what number?
Practice: Write an equation for each, then solve.
1.
What is 45 percent of 300?
x = .45(300)
135
2. What percent of 20 is 8?
x(20) = 8
40%
3. 64 is what percent of 800?
64 = x(800)
8%
4. 12 percent of what number is 90?
.12(x) = 90
750
5. 40 percent of 85 is what number?
.40(85) = x
34
Answer Key
Application Example:
One pair of jeans has a regular price of $24.99 and has a discount of 25% off.
A second pair has a regular price of $19.99 and has a discount of 10% off.
Which pair ends up being cheaper with the discounts?
Go on to the next page to continue.
Application Example:
One pair of jeans has a regular price of $24.99 and has a discount of 25% off.
A second pair has a regular price of $19.99 and has a discount of 10% off.
Which pair ends up being cheaper with the discounts?
First, we have to put into words what we are trying to find for each
pair of jeans. Then we can translate each into an equation.
1. What is 25% of 24.99?
2. What is 10% of 19.99?
translate
translate
x = .25(24.99)
x = . 10(19.99)
solve
solve
$6.25 off
$2.00 off
Go on to the next page to continue.
Application Example:
One pair of jeans has a regular price of $24.99 and has a discount of 25% off.
A second pair has a regular price of $19.99 and has a discount of 10% off.
Which pair ends up being cheaper with the discounts?
First, we have to put into words what we are trying to find for each
pair of jeans. Then we can translate each into an equation.
1. What is 25% of 24.99?
2. What is 10% of 19.99?
translate
translate
x = .25(24.99)
x = . 10(19.99)
solve
solve
$6.25 off
$2.00 off
For this example, we want to know which pair is overall cheaper, so
we need to subtract from the original prices.
1st pair: $24.99 – $6.25 = $18.74
2nd pair: $19.99 – $2.00 = $17.99
The second pair ends up being cheaper.
Practice: Write an equation for each, then solve.
1.
After a 15% discount, the cost of a car is
reduced by $6,799. What was the original
cost?
2.
30 out of 170 wedding guests sent an “no”
RSVP back. What percent of the guests who
were invited are not attending?
Practice: Write an equation for each, then solve.
Answer Key
1.
2.
After a 15% discount, the cost of a car is
reduced by $6,799. What was the original
cost?
“15% of what original amount is 6799?”
.15(x) = 6799
$45,326.67
30 out of 170 wedding guests sent an “no”
RSVP back. What percent of the guests who
were invited are not attending?
“30 is what percent of 170?”
30 = x(170)
about 17.6%