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21 February, 05:09

1. Twice a number added to a smaller number is 5. The difference of 5 times the smaller number and the larger number is 3. Let x represent the smaller number and y represent the larger number. Which equations represent the situation?

A number, y, is equal to the difference of a larger number and 3. The same number is one-third of the sum of the larger number and 9. Which equations represent the situation?

2.

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  1. 21 February, 07:27
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    1) ok so X is smaller than Y

    2Y + X = 5

    5X - Y = 3

    we need the equations to equal Y for simplicity

    y = (5-x) / 2

    Y = 5x - 3

    now equate the equations to each other

    (5-x) / 2 = 5x - 3

    *multiply 2 to both sides

    5-x = 10x - 6

    *solve for x

    11 = 11X

    X = 1

    **plug X back into any of the original equations

    Y = 5 (1) - 3

    y = 2

    * * x = 1 and y = 2

    2) ok so now the larger number x

    y = x-3

    y = (x+9) / 3

    **same steps as before

    x-3 = (x+9) / 3

    *multiply 3 to both sides

    3x-9 = x + 9

    2x=18

    x=9

    plug back into original equation

    y = (9) - 3

    y = 6

    so x=9 and y=6
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