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22 July, 02:41

The number of cattle at a farm is 660. This is a 10% decrease in the number of cows, a 50% increase in the number of bulls, and an overall increase of 10% in the total number of cattle from last year. How many cows and bulls were there each at the farm last year

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  1. 22 July, 03:46
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    let x = cows last year

    let y = bulls last year

    x + y = last years total

    0.9x + 1.5y = 660 (this year's total)

    1.1 (x+y) = 660 = 1.1x + 1.1y = 660

    so:

    0.9x + 1.5y = 1.1x + 1.1y

    subtract 0.9x from each side:

    1.5y = 0.2x + 1.1y

    subtract 1.1y from each side

    0.4y = 0.2x

    to make x 1 multiply both sides by 5

    2y = x

    substitute for x in one of the original problems:

    since they had 660 this year and that number is 10% higher than last year, then we had 600 total last year.

    So:

    600 = x + y

    substitute into that one with the 2y = x

    600 = 2y + y

    600 = 3y

    200 = y

    then 600 - y = x

    so 600 - 200 = x

    400 = x

    So you had 400 cows and 200 bulls last year
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