3B Mathematics Ch.7 Percentage

3B Mathematics Ch.7 Percentage

By Wang Kwong

Important Formulas!

1. Change = New value - Original value

2. ​Percentage change = (New value - Original value) / Original value x 100%

3. New value = Original value x (1 + Percentage change)​

Subject | Mathematics

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Example

Find the percentage change when a value changes from 156 to 195.

156 is an original value or a new value?

195 is an original value or a new value?

Which formula do we ​need?

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Example

Find the percentage change when a value changes from 156 to 195.

156 is an original value.

195 is a new value.

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Percentage change

= (New value - Original value) / Original value x 100%

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Find the percentage change when a value changes from 360 to 306.

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When 50 increases by 6%, find the new value.

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When a number decreases by 45%, it becomes 374. Find the original number.

Continuous percentage change

Kay’s weight was 75 kg in March. Her weight decreased by 4% in April, then increased by 5% in May. Find Kay’s weight in May.

Subject | Maths

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Continuous percentage change

Kay’s weight was 75 kg in March. Her weight decreased by 4% in April, then increased by 5% in May. Find Kay’s weight in May.

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x Weight in May = 75 x (1 - 4% + 5%)​

√​ Weight in May = 75 x (1 - 4%) x (1 + 5%)

*​ (1 - 4%) and (1 + 5%) are decay and growth factor

Subject | Maths

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The price of a chair was $880. The price was first increased by 15%, and then decreased by 10%. Find the new price of the chair.

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Martin invests $10 000 in a fund. He gains 6% in the first month, and then loses 3% in the second month. Find the percentage change in Martin’s investment over these two months.

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A number increases by 28% and then decreases by 50%. If the resulting number is 32, find the original number.

Continuous percentage change

New value = Original value x (1 + r₁%) x (1 + r₂%) x (1 + r₃%) x ...

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if r₁% = r₂% = r₃% = ... = r%?

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​New value = Original value x (1 + r%)ⁿ

Subject | Subject

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The present value of an antique vase is $10 000. If its value increases by 12% each year, what will its value be after two years?

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The present price of a pair of shoes is $2300. If its price increases by 2% each month, what will its price be after four months?

            (Give the answer correct to the nearest dollar.)

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The number of a certain kind of germ in a room increases by 100% every 4 hours. If there are 60 germs initially, how many germs will there be in the room 24 hours later?

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The present price of a machine is $680 000. The price of the machine decreases by 6% every quarter. What will its price be after 2 years?

       (Give the answer correct to the nearest thousand dollar.)