CONFIDENTIAL 1

Grade 8 Algebra1Grade 8 Algebra1

Applications ofApplications ofPercentsPercents

CONFIDENTIAL 2

Warm UpWarm Up

1) Find 75% of 60.

2) Find 115% of 80.

3) What percent of 40 is 25?

4) What percent of 225 is 135?

5) 56 is what percent of 20?

CONFIDENTIAL 3

Applications of Percent

Sales representatives use percents to calculate their total pay.

We can apply percent concepts to find the discount and sale price of an item. The discount rate is given as a percent.

Percent concepts can be applied to compute percent increase and percent decrease of various items.

We can apply percent concepts to solve problems of the form "One number is some percent of another number." by identifying the given information, setting up a proportion, and solving for the unknown value.

CONFIDENTIAL 4

A commission is money paid to a person or a company for making a sale. Usually the commission

is a percent of the sale amount.

Interest is the amount of money charged for borrowing money, or the amount of money earned when saving

or investing money. Principal is the amount borrowed or invested. Simple

interest is interest paid only on the principal.

Formula for Simple Interest Paid Annually

Simple Interest, I = P × r × t

Principal Interest rate peryear as a decimal

Time in years

CONFIDENTIAL 5

A) Daniela earns a base salary of $40,000 plus a 2.5% commission on sales. Her total sales one year were

$800,000. Find her total pay for the year.

total pay = base salary + commission

= base salary + % of total sales

= 40,000 + 2.5% of 800,000

SOLUTION:

Next page

Write the formula for total pay.

Write the formula for commission.

Substitute values given in theproblem.

Business Application

CONFIDENTIAL 6

= 40,000 + 2.5 of 800,000 100

= 40,000 + (0.025)(800,000)

Write the percent as a decimal.

= 40,000 + 20,000

Add.

= 60,000

Daniela total pay was $60,000.

CONFIDENTIAL 7

1) A telemarketer earns $350 per week plus a 12% commission on sales. Find her total pay for a week

in which her sales are $950.

Solve:

Now you try!

CONFIDENTIAL 8

Finance Application

A) Find the simple interest paid annually for 3 years on a $1200 loan at 15% per year.

I = P r t

I = (1200) (0.15) (2)

I = 540

SOLUTION:

Write the formula for simple interest.

Substitute known values. Write the interest rate as a decimal.

The amount of interest is $540.

CONFIDENTIAL 9

B) After 3 months the simple interest earned annually on an investment of $7000 was $63. Find the interest rate.

I = P r t

63 = (700) (r) (3) 12

SOLUTION:

Write the formula for simple interest.

Substitute known values.

When you are using the formula I = P r t to find simple interest paid annually, t represents time in years.

One month is 1 year. In the given problem, t =3 . 12 12

Next page

CONFIDENTIAL 10

63 = 1750r

The interest rate is 3.6%.

Multiply 7000 (3) . 12

63 = 1750r1750 1750

0.036 = r

Since r is multiplied by 1750, divide both sides by 1750 to undo the multiplication.

CONFIDENTIAL 11

1) Find the simple interest earned after 2 years on an investment of $3000 at 4.5% interest earned annually.

Solve:

Now you try!

2) The simple interest paid on a loan after 6 months was $306. The annual interest rate was 8%. Find the principal.

CONFIDENTIAL 12

A tip is an amount of money added to a bill for service. It is usually a percent of the bill before sales tax is added.

Sales tax is a percent of an item’s cost.

Sales tax and tips are sometimes estimated instead of calculated exactly. When estimating percents, use percents that you can calculate mentally.

• Find 10% of a number by moving the decimal point one place to the left.

• Find 1% of a number by moving the decimal point two places to the left.

•Find 5% of a number by finding 1 of 10% of the number. 2

CONFIDENTIAL 13

Estimating with Percents

A) The dinner check for Maria’s family is $67.95. Estimate a 15% tip.

Step 1: First round $67.95 to $70.

SOLUTION:

Move the decimal point one place left.

The tip should be about $10.50.

Step 2: Think: 15% = 10% + 5% 10% of $70 = $7.00

Step 3: Think: 5% = 10% ÷ 2 = $7.00 ÷ 2 = $3.50

Step 4: 15% = 10% + 5% = $7.00 + $3.50 = $10.50

CONFIDENTIAL 14

Estimating with Percents

B) The sales tax rate is 6.25%. Estimate the sales tax on a shirt that costs $29.50.

Step 1: First round 6.25% to 6% and $29.50 to $30

SOLUTION:

Move the decimal point two places to the left.

The sales tax is about $1.80.

Step 2: Think: 6% = 6 (1%) 1% of $30 = $0.30

Step 3: 6% = 6 (1%) = 6 ($0.30) = $1.80

CONFIDENTIAL 15

Now you try!

1) Estimate a 15% tip on a check for $21.98.

Solve:

2) Estimate the tax on shoes that cost $68.50 when the sales tax rate is 8.25%.

CONFIDENTIAL 16

Some more examples

A) Two candidates A and B contest an election. A gets 46% of the valid votes and is defeated by 1600 votes.

Find the total number of valid votes cast in the election?

SOLUTION:

A gets 46% of the valid votes.

B gets (100 – 46)% = 54% of the valid votes.

Therefore, % difference if the votes by which A is defeated is = 54% - 46% = 8%.

Total number of valid votes cast = 100 ×1600 = 20,000 8

Total number of valid votes cast is 20,000

8% of the total valid votes cast = 1600.

i.e. 8 of the total votes = 1600. 100

CONFIDENTIAL 17

B) My income was increased by 10% and later decreased by 10%. What is the total change in the percent in my income?

SOLUTION:

Let my income be $100.

10% increase means that my income becomes $110.

Decreased income = $110 - $ 10 × 110 100 = $110 - $11 = $ 99.

% change in income = Change in income ×100% original income = $100 - $99 ×100% = 1% $100

The percent in my income is 1%.

CONFIDENTIAL 18

Now you try!

1) What percent of votes are in favor of a candidate if 25 persons vote for him and 45

persons vote against him?

Solve:

CONFIDENTIAL 19

Assessment

1) A sales representative earns a 2.5% commission on sales. Find the commission earned

when the total sales are $80,700.

2) A man spends 45% of his income and saves $2640 in a month. What is his monthly income?

3) Karen earns a salary of $28,600 per year plus a 4.25% commission on sales. Find her total

salary for a year when the sales are $310,000.

CONFIDENTIAL 20

4) Find the amount of simple interest earned after 2 years on $480 invested at a 7% annual interest rate.

5) Find the number of years it would take for $1200 to earn simple interest of $324 at an annual interest

rate of 6% per year.

6) Find the total amount owed after 6 months on a loan of $900 at an annual interest rate of 8.5%.

7) Estimate the tip on a $42.65 check using a tip rate of 15%.

CONFIDENTIAL 21

8) Estimate the tax on a $198 stereo when the sales tax is 5.25%.

9) The weight of the box by mistake was written as 21 kg, while it was 25 kg. What is the error %.

10) A boy remains awake for 16 hrs a day. For what percentage of the time does he sleep?

CONFIDENTIAL 22

A commission is money paid to a person or a company for making a sale. Usually the commission

is a percent of the sale amount.

Interest is the amount of money charged for borrowing money, or the amount of money earned when saving

or investing money. Principal is the amount borrowed or invested. Simple

interest is interest paid only on the principal.

Formula for Simple Interest Paid Annually

Simple Interest, I = P × r × t

Principal Interest rate peryear as a decimal

Time in years

Let’s review

CONFIDENTIAL 23

A) Daniela earns a base salary of $40,000 plus a 2.5% commission on sales. Her total sales one year were

$800,000. Find her total pay for the year.

total pay = base salary + commission

= base salary + % of total sales

= 40,000 + 2.5% of 800,000

SOLUTION:

Next page

Write the formula for total pay.

Write the formula for commission.

Substitute values given in theproblem.

Business Application

review

CONFIDENTIAL 24

= 40,000 + 2.5 of 800,000 100

= 40,000 + (0.025)(800,000)

Write the percent as a decimal.

= 40,000 + 20,000

Add.

= 60,000

Daniela total pay was $60,000.

review

CONFIDENTIAL 25

Finance Application

A) Find the simple interest paid annually for 3 years on a $1200 loan at 15% per year.

I = P r t

I = (1200) (0.15) (2)

I = 540

SOLUTION:

Write the formula for simple interest.

Substitute known values. Write the interest rate as a decimal.

The amount of interest is $540.

review

CONFIDENTIAL 26

Estimating with Percents

A) The dinner check for Maria’s family is $67.95. Estimate a 15% tip.

Step 1: First round $67.95 to $70.

SOLUTION:

Move the decimal point one place left.

The tip should be about $10.50.

Step 2: Think: 15% = 10% + 5% 10% of $70 = $7.00

Step 3: Think: 5% = 10% ÷ 2 = $7.00 ÷ 2 = $3.50

Step 4: 15% = 10% + 5% = $7.00 + $3.50 = $10.50

CONFIDENTIAL 27

Estimating with Percents

B) The sales tax rate is 6.25%. Estimate the sales tax on a shirt that costs $29.50.

Step 1: First round 6.25% to 6% and $29.50 to $30

SOLUTION:

Move the decimal point two places to the left.

The sales tax is about $1.80.

Step 2: Think: 6% = 6 (1%) 1% of $30 = $0.30

Step 3: 6% = 6 (1%) = 6 ($0.30) = $1.80

review

CONFIDENTIAL 28

Some more examples

A) Two candidates A and B contest an election. A gets 46% of the valid votes and is defeated by 1600 votes.

Find the total number of valid votes cast in the election?

SOLUTION:

A gets 46% of the valid votes.

B gets (100 – 46)% = 54% of the valid votes.

Therefore, % difference if the votes by which A is defeated is = 54% - 46% = 8%.

Total number of valid votes cast = 100 ×1600 = 20,000 8

Total number of valid votes cast is 20,000

8% of the total valid votes cast = 1600.

i.e. 8 of the total votes = 1600. 100

review

CONFIDENTIAL 29

B) My income was increased by 10% and later decreased by 10%. What is the total change in the percent in my income?

SOLUTION:

Let my income be $100.

10% increase means that my income becomes $110.

Decreased income = $110 - $ 10 × 110 100 = $110 - $11 = $ 99.

% change in income = Change in income ×100% original income = $100 - $99 ×100% = 1% $100

The percent in my income is 1%.

review

CONFIDENTIAL 30

You did a great job You did a great job today!today!