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紫雪 asked in 科學及數學數學 · 1 decade ago

怎可清楚計算出step?

1)Anthony's weight increased by 5% last month but has decreased by 5% this month. What is the percentage change in Anthony'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.

2 Answers

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  • 1 decade ago
    Favorite Answer

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

    1, let Anthony'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'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 decade ago

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

    let Anthony'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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