2. Petra deposited $250 into a bank account. After
one year, she received $30 in interest and now
had $280 in the account. What percent interest
did she receive from the bank?
Solving Percent Problems
28
70
amount of increase
original amount
When Jim was exercising, his heart rate went from 70 beats per
minute to 98 beats per minute. What was the percent increase?
First find the amount of change.
3. Percent Increase and Decrease
The actual increase = 11.7 – 7.8 = 3.9 lb.
The percentage increase =
3.9
7.8
= 50%
What is the baby’s percentage increase in weight?
A baby weighs 7.8 lb. at birth. After 6 weeks
the baby’s weight has increased to 11.7 lb.
4. What is the original price of the jeans?
I bought some jeans in a sale. They had
15% off and I only paid $25.50 for them.
5. The actual decrease = 25 –17 = $8
The percentage decrease =
8
25
= 32%
What is the percentage decrease?
6. Her actual profit = 99 – 45 = 54
Her percentage profit =
54
45 = 120%
What is her percentage profit?
A shopkeeper buys chocolate bars wholesale at a
price of .45 each. She then sells the chocolate bar in
her shop at .99 each.
7. A Proportion is an equation that two ratios are equal. To
determine if ratios are equal, cross-multiply and check for
equality. 2/5 and 6/15 are proportional ratios.
We have used the Percent Proportion to solve percent problems,
but there are other problems which do not involve percents.
A Ratio is a comparison of two numbers by division. Ratios can
be expressed by: 4:3, or 4 to 3, or 4/3.
A Rate is the comparison (ratio) of two different units of
measure. Ex: miles per hour, gallons an hour, dollars a pound
8. Example 1: Ben runs 4 miles in 45 minutes. If he only has 30
minutes, how far can he run?
Set up a proportion and solve: 4 (miles) = x (miles)
45 (min.) 30 (min.)
Example 2: Jill can jump rope 420 times in 2.5 minutes. At this
rate, how many can she do in 7 minutes?
Set up a proportion and solve: 402(jumps) = x (jumps)
2.5 (min.) 7 (min.)
9. You can use proportions to find dimensions of
objects that are difficult to measure directly…
In the Figure below, ABC ~ (is similar) DFE.
C
A
21 cm
18 cm
15 cm
B
x
D F
10 cm
E
Set up the proportion:
Find the length of side DE
15 = 21
10 x
10. The shadow of a 4 ft. tall mailbox is 3 ft. long.
If the shadow of a tree is 36 ft. long, how tall
is the tree?
height
shadow
height
shadow
=
You must be careful to place the
same quantities in corresponding
positions in the proportion
H
36
4
3 =
11. Write the ratio 15 bikes to 9 skateboards
in its simplest form.
15
9
5
3
=
15 ÷ 3
9 ÷ 3
Write the ratio
as a fraction.
= = Simplify.
The ratio of bikes to skateboards is , 5:3, or 5 to 3.
5
3
bikes
skateboards
12. The ratio of the number of bones in a human’s ears to the
number of bones in the skull is 3:11. There are 22 bones in
the skull. How many bones are in the ears?
Write a ratio comparing bones in ears
to bones in skull.
Write a proportion. Let x be the
number of bones in ears.
Since x is divided by 22, multiply
both sides of the equation by 22.
There are 6 bones in the ears.
13. The ratio of games lost to games won for a baseball team
is 2:3. The team has won 18 games. How many games did
the team lose?
The team lost 12 games.
Write a ratio comparing games lost to games won.
Write a proportion. Let x be the number of games lost.
Since x is divided by 18, multiply
both sides of the equation by 18.
14. The ratio of games lost to games won for a baseball team
is 2:3. The team has played 45 games. How many games
did the team lose?
Write a ratio comparing games lost to total games
Write a proportion. Let x be the number of games lost.
15.
16. Unit rate:
75 miles,
1 hour
or 75 MPH
225
3
=
75
1
Mel drove 225 miles in three hours.
Which quantity do we want to equal 1, that is per mile or
per hour?
Since we want miles per hour, divide top & bottom by 3
225
3
17. 1. A 64 oz. Apple Juice costs $1.35. Find the unit rate.
2. A 12 slice pizza costs $9.00. Find the unit rate.
3. Which is the better buy: A 12 oz. bottle of juice
for $0.85, or an 8 oz. can of juice for $0.50?
Which unit, (oz. or $) do we want to reduce to 1?
