Week 3: Solving Percent Problems

Week 3: Solving Percent Problems

Calculating the percent of a number using the percent proportion:

Solve Each Proportion:

What is 16% of 80? → 16%(is)100% = x 80(of)

92 is what percent of 70? → 9270 = x%100

56 is 38% of what number? → 56x = 38%100

Solving Percent Word Problems.

Remember: You can also find the percent of a number by changing the percent to a decimal and multiplying..

Sale Prices & Discounts

à The rate is usually given as a percent.

To find the discount, multiply the rate by the original price.

To find the sale price, subtract the discount from original price.

Example1: A sweater is marked down 33%. Its original price was $40.00 What is the new price of the sweater?

$40.00
Original Price of Sweater
Discount
33% of $40.00
= $13.20 / Sale Price
67% of $40.00
= $26.80

Example 2:. A shirt is on sale for 40% off. The sale price is $12. What was the original price? What was the amount of the discount?

Discount
40% of original price / Sale Price - $12
60% of original price
Original Price (p)

--- If we saved 40%, that means we paid for 60% of the original price.

-- Therefore, you must find solve : 60% of what number would be 12.

SALES TAX (Same procedure for TIP):

à Must find the tax and then add it to the total

à Remember a percent that is less than 10% as a decimal will always be 0.0______

5% = .05 4% = 0.04 8.5% = .085

à If the cost already includes the tax, that means the percent is MORE than 100%

Example 1: Bob bought a desk that cost $450. If an 8% sales tax is added to the cost of the desk, how much did he have to pay all together?

Equation:

8% of $450

= .08(450)

= $36 à this is the tax

$36 + $450 = $486 à this is the total

Proportion

8100=x450

100x = 3,600

x = 36

$450 + 36 = $486

Example 2: Sam pays $31.50 for a jacket. The amount includes a 5% sales tax. How much is the jacket without tax?

à If the amount already includes the tax, that means it is more than 100% of the original cost!

Price of Jacket without tax
100% / Tax
5%
Price of Jacket + Tax = 105%
= $31.50

105% = 1.05

Let p = the price of the jacket without tax

1.05p = 31.50

p = 30

The price of the jacket was $30 before tax.

Percent Change

à the amount of change is how much something increase or decreased by

amount of changeoriginal=% change100

Example 1) Last year, Harold earned $250 a month at his after‐school job. This year, his after‐school earnings have increased to $300 per month. What is the percent increase in his monthly after‐school earnings?

300-250250 =x100 à 50250=x100

5,000 = 250x

20 = x Harold increase in salary was 20%

Example 2) Gas prices are projected to increase 124% by April 2015. A gallon of gas currently costs $4.17. What is the projected cost of a gallon of gas for April 2015?

You Try:

1) Donna gets 4 problems wrong on her quiz. Her score is 85%. How many questions are on the quiz?

2) A store owner buys backpacks at a certain price and sells them at a higher price. If she pays $21 for a backpack and adds a 40% markup on the price she paid, what is the selling price

3) A store spends $10 for each pair of Brand X jeans and adds a 120% markup to the cost. What is the selling price of the jeans. Circle the correct answer.

$11.20
$12.00
$22.00
$130

4) The price of a book is $6.00 and the sales tax is 5%. What is the total cost of the book plus tax?

$0.30
$5.70
$6.05
$6.30

5) Trent borrows $250 and pays 5.5% simple interest each year. If he pays back the money in one year, what is the total amount that he pays?

$13.75
$236.25
$263.75
$387.50

6) Elena gets a base pay of $1,500 per month. She also earns a commission of 8% of the total sales dollars that she makes. What are Elena’s earnings for a month in which she has sales of $32,000?

$1,620
$2,560
$4,060
$27,100

7) On Thursday, 30 students went to after school tutoring. On Friday, 6 students went. What is the percent decrease in the number of students who went to tutoring?

a. 20%

b. 80%

c. 400%

d. 500%

8) Mr. Gibson usually sells umbrellas in his store for $8.00 each. However, on rainy days, he increases the price by 75%. How much does he charge for an umbrella on a rainy day?

9) The seventh graders set a goal to collect 400 cans for their school’s food drive. They collected 420 cans. What percent of their goal did they collect? (MCC.7.RP.3)

A. / 60% / B. / 105% / C. / 110% / D. / 120%

10) The original price of a monitor was $160. It was on sale at a 20% discount. Later, the price of the monitor was reduced by an additional 50% of the sale price. What was the final price of the monitor?

A. / $64 / B. / $70 / C. / $80 / D. / $128

From 2012 State Test: