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# 怎可清楚計算出step?

1)Anthony&#39;s weight increased by 5% last month but has decreased by 5% this month. What is the percentage change in Anthony&#39;s weight in these two months?

2)The length and the width of a rectangular carpet have decreased by 10% and 7% respectively after washing. Find the decrease in the area of the carpet.

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1)Anthony&#39;s weight increased by 5% last month but has decreased by 5% this month. What is the percentage change in Anthony&#39;s weight in these two months?

1, let Anthony&#39;s weight be ‘a”

The weight of last month

a x (1+5%)

= a x 1.05

=1.05a

The weight of this month

1.05a x (1-5%)

=1.05a x 0.95

=0.9975a

The percentage change

0.9975a x 100%

1.05a

= 0.95x100%

=95%

the percentage change in Anthony&#39;s weight in these two month is 5%

2)The length and the width of a rectangular carpet have decreased by 10% and 7% respectively after washing. Find the decrease in the area of the carpet.

Let the Length be ‘a’ and width be ‘b’

The area before washing

. a x b = ab

The area after washing

[a x (1-10%)] x [ b x (1-7%)]

=( a x 0.9) x (b x 0.93)

=0.9a x 0.93b

=0.837ab

The decrease in area

1-0.837ab x 100%

1ab

= 0.163ab x 100%

1ab

= 16.3%

the decrease in the area of the carpet is 16.3%

• 1)Anthony&#39;s weight increased by 5% last month but has decreased by 5% this month. What is the percentage change in Anthony&#39;s weight in these two months?

let Anthony&#39;s original weight be x

the new weight after 2 months = x (1.05) (.95) = 0.9975x

the percentage change = (0.9975x-x)/x * 100% = -0.25%

The length and the width of a rectangular carpet have decreased by 10% and 7% respectively after washing. Find the decrease in the area of the carpet.

original area = lw

new area = 0.9l (0.93w) = 0.837lw

decrease in area = - (0.837lw - lw) / lw * 100% = 16.3%

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