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Step 9: Proportional reasoning

Percent change, tax, and interest

Step 9 · Proportional reasoning topics

Find a percent of a number and the whole from a part, work out percent increases and decreases, and use percents for sales tax, tips, discounts and simple interest.

Percent of a number

Percent means out of 100. To find a percent of a number, write the percent as a decimal and multiply.

Example: Percent of a number

What is 35% of 80?

  1. 35% = 0.35.
  2. 0.35 × 80 = 28.

Answer28

A whole cut into 20 equal parts: 35% is 7 of them, because each part is 5%.

Example: Finding the whole

12 is 30% of what number?

  1. 0.3 × n = 12.
  2. n = 12 ÷ 0.3 = 40.

Answer40

Percent increase and decrease

A percent change compares the change with the amount you started with.

percent change=new−oldold×100%\text{percent change} = \frac{\text{new} - \text{old}}{\text{old}} \times 100\%

Example: Percent increase

A game's price goes from $40 to $50. What is the percent increase?

  1. The change is 50 − 40 = 10.
  2. 10 ÷ 40 = 0.25.
  3. 0.25 is 25%.

Answer25%

Example: Percent decrease

A $60 jacket is 15% off. What is the sale price?

  1. 15% of 60: 0.15 × 60 = 9.
  2. 60 − 9 = 51.
  3. Or in one step: you pay 85%, and 0.85 × 60 = 51.

Answer$51

Tax, tips and simple interest

Sales tax and tips are percents added on to a price. Simple interest is a percent of the money borrowed or saved, paid for each year.

Example: Sales tax

A $24 book has 6% sales tax. What is the total?

  1. 0.06 × 24 = 1.44.
  2. 24 + 1.44 = 25.44.

Answer$25.44

Example: A tip

A meal costs $45. What is a 20% tip?

  1. 10% is $4.50.
  2. 20% is twice that: $9.

Answer$9

I=PrtI = Prt

I is the interest, P the principal (the money you start with), r the yearly rate as a decimal, and t the time in years.

Example: Simple interest

$500 is saved at 3% simple interest for 4 years. How much interest does it earn?

  1. Each year: 500 × 0.03 = 15.
  2. Four years: 15 × 4 = 60.

Answer$60

Try it yourself

Work each one on paper first, then open the answer to check.

  1. What is 15% of 60?

    Show answer

    9

  2. 18 is 45% of what number?

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    40

  3. A price rises from $25 to $30. What is the percent increase?

    Show answer

    20%

  4. A town's population falls from 8,000 to 7,600. What is the percent decrease?

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    5%

  5. What is the total for an $80 helmet with 7.5% sales tax?

    Show answer

    $86

  6. How much simple interest does $1,200 earn at 5% a year for 3 years?

    Show answer

    $180

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