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Math Help - Daily wage word problem - with insufficient data?

  1. #1
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    Daily wage word problem - with insufficient data?

    Ann's daily wage is $10 less that Bill's. So she has to work 4 days more than Bill to earn the same amount of money as Bill. If Bill earns $480, find Ann's daily wage.

    I created a table like so,

    Ann Bill
    Wage (x-10) x
    Days (y+4) y
    Salary (x-10)(y+4) 480

    Then, using the equation,

    (x-10)(y+4) = 480

    I got,
    2x - 5y = 20

    I can't seem to figure out how to proceed. What am I missing? Do I have to make an assumption of the number of days?

    Thanks.
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  2. #2
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    Quote Originally Posted by mathguy80 View Post
    Ann's daily wage is $10 less that Bill's. So she has to work 4 days more than Bill to earn the same amount of money as Bill. If Bill earns $480, find Ann's daily wage.

    I created a table like so,

    Ann Bill
    Wage (x-10) x
    Days (y+4) y
    Salary (x-10)(y+4) 480

    Then, using the equation,

    (x-10)(y+4) = 480

    I got,
    2x - 5y = 20

    I can't seem to figure out how to proceed. What am I missing? Do I have to make an assumption of the number of days?

    Thanks.
    All your considerations and calculations are correct.

    You only forgot that Bill earns some money too:

    x \cdot y = 480~\implies~y = \dfrac{480}x

    Replace the variable y in your equation by the term above and solve for x.
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  3. #3
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    Doh! Completely missed that!

    So got a quadratic equation, and solving for x, discarded the negative value, Ann's share is $30.

    Thanks for your help.
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