This document contains examples of solving percent problems using equations. It discusses writing equations to solve problems involving percent of a number, percent increase or decrease, sales tax rate, commission rate, and discount rate. Various word problems are presented along with the equations and step-by-step solutions. The document provides instruction on translating word problems into mathematical equations in order to calculate unknown values related to percentages.

1. John Paul L. Hablado
Numerical Reasoning and Ability
Topic: Percent, Discount and Commission
Mathematics, Science and Professional Education Instructor Guimaras State College

2. Percent Problems with Equations
Translate the following statements to equations:
8 is what percent of 48?
8  x  48
2.6 is 40% of what number?
6.2  %40  x
What number is 90% of 0.045?
x  %90  045.0

3. Percent Problems with Equations
Write the equation and solve.
What number is 25% of 90?
90x = 25% .
90x = 0.25 .
x = 22.5

4. Percent Problems with Equations
Write the equation and solve.
15% of what number is 2.4?
2.415% =x.
0.15
2.40.15 =x
2.40.15
=
x
x = 16
0.15

5. Percent Problems with Equations
Write the equation and solve.
What percent of 90 is 27?
27x =90.
90
2790x =
2790
=
x
x = 0.3
90
x = 0.3
x = 30%
. 100%

6. Percent Problems with Equations
Write the equation and solve.
18 is 4.5% of what number?
x18 .
4.5%=
0.045
0.045x18 =
0.045x18
=
x=400
0.045

7. Applications of Percent
The length of the Appalachian Trail is 2174 miles. Twenty-
five percent of the length is in the state of Virginia. How
many miles are in Virginia?
x2174 =25%.
x2174 . 0.25 =
x543.5 =
miles

8. Applications of Percent
There are currently 130,000 nurses in the state of Florida.
Of those nurses, 34,000 are new. What is the percentage of
new nurses? Round to the nearest whole percent.
34,000130,000 =x.
34,000130,000 x =
x
130,000 130,000
= 0.261
x = 0.261 . 100%
x = 26.1%
x = 26%

9. Applications of Percent
In 2000, there were 240 million vehicles on the road in the
United States. In seven years, the total was increased by
3%. (a) What was the increase in the number of vehicles
in the seven years? (b) What was the total number of
vehicles in 2007?
3%240 = x.
0.03240 . x
7.2
=
= x
million vehicles
7.2240 +
247.2
(a) (b)
million vehicles

10. Applications of Percent
Percent of Increase:
285
amount of increase:
=
333 – 285 =
.48
0.1684
285
=
48
increase
100% 16.84% = 16.8%
amount of increase
original amount
. 100%
The number of people attending a local play increased
from 285 on Friday to 333 on Saturday. Find the percent
of increase and round to the nearest tenth percent.
original amount:
.
100%

11. Applications of Percent
Percent of Decrease:
20,200
amount of decrease:
=
20,200 – 18483 =
.1717
0.085
20,200
=
1717
decrease100% 8.5%
amount of decrease
original amount
. 100%
A town with a population of 20,200 in 1995 decreased to
18,483 in 2005. What is the percent decrease? Round to
the nearest tenth percent, if necessary
original amount:
.
100%

12. Percent and Problem Solving: Sales Tax,
Commission, and Discounts
Sales Tax and Total Price:
Sales Tax .purchase price= tax rate as a decimal
Total Price +purchase price= sales tax
purchase price:
₱21.00
tax rate: 7%
Sales Tax = ₱ 21.00 . 0.07
Sales Tax = ₱ 1.47
= 0.07
Total Price = ₱ 21.00 + ₱ 1.47
Total Price = ₱ 22.47

13. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
= 5.0915
Sales Tax
=59.90 + 5.098.5%
= 64.99
An artificial holiday tree costs ₱ 59.90. If the tax rate is
8.5%, what are the sales tax and the total price. Round the
sales tax to the nearest cent.
Total Price
.
=59.90
=59.90 .
0.085
=₱ 5.09
= ₱ 64.99

14. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
=x
.
x
100%
If a car costs ₱ 18,500 and the sales tax is ₱ 1665, what is
the sales tax rate?
.18500
18500 x 1665
18500 18500
0.09
= 1665
=x 0.09
=x 9%
=

15. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
Commission . commission rate as a decimal= total sales
Total sales: ₱ 500.00 Commission rate: 15%
Commission = 500.00 . 0.15
Commission = ₱ 75.00
= 0.15

16. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
=3143.712
Commission
6.6%
A sales representative from a paper products company sold
₱ 47,632 worth of products during a month. The sales
commission rate was 6.6%. What was the commission?
.
=47,632
=47,632 .
0.066
=₱ 3,143.71

17. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
x
=x
A salesperson earns ₱ 645 for selling ₱ 4300 worth of
appliances. What is the commission rate?
.
4,300
4,300 x 645
4,300 4,300
=
645
0.15
.
100%
x = 15%
x = 0.15
=

18. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
Discount and Sales Price:
Amount of Discount .original price= discount rate as a decimal
original price: ₱ 160.00 discount rate: 28%
Amount of discount = ₱ 160.00 . 0.28
Amount of discount= ₱ 44.80
= 0.28
Sales Price –original price= amount of discount
Sales Price = 160.00 – 44.8
Sales Price = ₱ 115.20

19. Percent and Problem Solving:
Sales Tax, Commission, and Discounts
=245.00
Amount of discount
=700.00 – 245.0035%
=455.00
A discontinued washer/dryer combination is advertise on
sale for 35% off the original price of ₱ 700. What are the
amount of discount and the sales price?
Sales Price
.
=700
=700 . 0.35
=₱ 245.00
=₱ 455.00