The document discusses various formulas for calculating percentages related to changes in price, quantity, or other values. It provides examples of using the percent change formula to calculate percentage increases or decreases when a value changes. The percent proportion formula is used when finding the percent of a fixed total. The document also covers formulas for calculating original prices based on marked up, discounted or final prices that have been increased or decreased by a certain percentage.

1. Today:
Percent Change Formula
Formulas for Price Mark-ups,
Discounts, Taxes, etc.
Test Results

2. When you need to find the percent of a set quantity (not
changing), then you can use the percent proportion to solve.
Example: Dwight missed 9 out of 12 free throws,
what percent did he make?
X = 3
100 12
However, when you want to find the percent of
something that has changed (price, population, quantity),
you then use the percent of change formula….

3. Finding Percent Increase & Decrease

4. Find each percent change. Tell whether it is a percent
increase or decrease.
= 25% Write the answer as a percent.
Simplify the fraction.
8 to 10 is an increase,
so a change from 8 to
10 is a 25% increase.
Change to a decimal.
From 8 to 10
= 0.25
Ex. 1A: Percent Increase and Decrease

5. Ex. 1B: Finding Percent Increase and Decrease
From 75 to 30
= 0.6
= 60% Write the answer as a percent.
Simplify the fraction.
75 to 30 is a decrease,
so a change from 75 to
30 is a 60% decrease.
Find the percent change. Tell whether it is a percent
increase or decrease.
Write as a decimal

6. 1. From 200 to 110
= 0.45
= 45% Write the answer as a percent.
Simplify the numerator.
Simplify the fraction.
200 to 110 is an decrease, so a change
from 200 to 110 is a 45% decrease.
Find the percent change. Tell whether it is a percent
increase or decrease.
Practice 1: Percent Increase and Decrease
Write as a decimal

7. 2. From 25 to 30
= 0.20
= 20% Write the answer as a percent.
Simplify the numerator.
Simplify the fraction.
25 to 30 is an increase, so a change
from 25 to 30 is a 20% increase.
Find each percent change. Tell whether it is a percent
increase or decrease.
Practice 2: Percent Increase and Decrease
Write as a decimal

8. These next four are grouped together, and are not really
four different formulas:
A. Original price or number is increased by a given percent.
B. Original price or number is decreased by a certain percent.
C. Finding original price after increase (mark-up).
D. Finding original price after decrease (discount).

9. New Price or number: Original • (1 + Decimal form
of the percent)
A. Original price or number is increased by a given percent.
Example: What is 20 increased by 20%?
20 • 1 = 20; 20 • .2 = 4; 20 + 4 = 24
B. Original price or number is decreased by a certain percent.
Original • the compliment of the
Decimal form of the percent
New Price or number:
Example: What is 25 decreased by 20%? 25•.8 = 20
Note: Whenever the original number or price is
known, the formula involves multiplication.

10. C. Finding original price after increase (mark-up).
This formula is used to find the original price of an item when the
price is known after increases such as taxes, tips, and markups.
Original Price: Price after increase
1 + percent of
The cost of lunch after
a 15% tip was $24.15.
What was the cost of
just the lunch?
$24.15/ 1.15 (1 +15%) = $21.00

11. D. This formula is used to find the original price of an item
after the price is discounted. (Original Price was Higher)
The selling price of an item discounted 20% is $19.20.
What was the original price?
$19.20
.8
Price before discount was $24.00
Original Price: discounted price
Compliment of discount percent
=
Note: Whenever the original number or price is not
known, the formula involves division.

12. The entrance fee at an amusement park is $35.
People over the age of 65 receive a 20% discount.
What is the amount of the discount? How much do
people over 65 pay?A discount is a percent decrease. The original price is
known, so we will multiply. The formula for a known
price that has decreased, is… multiply by the
compliment of the discount.
0.80(35) = 28 Find 80% of 35. This is the
amount you are paying.
Example 1:

13. The wholesale cost of a DVD is $7. The markup is
85%. What is the amount of the markup? What is the
selling price?
Method 1
A markup is a percent increase. So find $7 increased by 85%.
0.85(7) = 5.95
7 + 5.95 = 12.95
Find 85% of 7. This is the amount of the
markup.
Add to 7. This is the selling price.
Subtract from 12.95. This is the
amount of the markup.
12.95 ÷ 7 = 5.95
The amount of the markup is
$5.95. The selling price is
$12.95.
The selling price is 185% of the
wholesale price, 7.
100% + 85% = 185%
Find 185% of 7. This is the selling price.1.85(7) = 12.95
Practice 1:

14. A video game has a 70% markup. The wholesale cost is $9.
Find:
A) What is the selling price? B) The amount of the markup.
A markup is a percent increase. So find $9 increased by 70%.
1.70(9) = 15.30Find 170% of 9. This is the selling price
15.30 – 9 =
$6.30
This is the amount of the markup
The amount of the markup is $6.30.
The selling price is $15.30.
Practice 2:

15. A $220 bicycle was on sale for 60% off. Find the sale price.
100% – 60% = 40%
The bicycle cost 40% of the
original price.
0.40(220) = 88 Find 40% of 220.
The sale price is $88.
Practice 3:
Which type of problem is this, and what is the formula?

16. Original Price: Price after increase
1 + percent of
Practice 4
A pair of pants retails for $12.00. This is 50% above the
wholesale cost. What is the wholesale cost?
$12.00
.5
= $8.00
The formula to find the original price of an item that
has been marked up is….
What type of problem is this?

17. Last Practice
Problem
Blah blah blah discounted 30%. Blah blah now
$42.00. Blah Blah blah, find original price.
$42.00
.7
= $60.00
discounted price
Compliment of discount percent
The formula to find the original price of
an item that has been marked down is….
Type of problem?

18. To find the correct formula, ask yourself
two questions:
1. Is the original price known?
If yes, then A or B. If no, then C or D
2. Did the price go up or down from the
original. This will separate A from B & C
from D
Class Work: 2.8
(show all work)

19. Class Work: 2.8
(show all work)