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Thread: ratio problem

  1. #1
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    Thumbs up ratio problem

    Can this be put into an equation:

    Two numbers are such that if the first receives 60 from the second they are in the ratio 2:1, but if the second receives 100 from the first, the ratio is 1:3.

    What are the two numbers?

    Been experimenting but have gotten far. Thanks!
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  2. #2
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    Quote Originally Posted by aquajam View Post
    Can this be put into an equation:

    Two numbers are such that if the first receives 60 from the second they are in the ratio 2:1, but if the second receives 100 from the first, the ratio is 1:3.

    What are the two numbers?

    Been experimenting but have gotten far. Thanks!
    let x = first number , y = the second


    if the first receives 60 from the second they are in the ratio 2:1

    $\displaystyle \frac{x+60}{y-60} = \frac{2}{1}$


    if the second receives 100 from the first, the ratio is 1:3

    $\displaystyle \frac{x - 100}{y + 100} = \frac{1}{3}$


    solve the system of equations for x and y
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  3. #3
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    Sorry, I'm a bit rusty. Can help me solve it?
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  4. #4
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    $\displaystyle \frac{x+60}{y-60} = \frac{2}{1}$

    $\displaystyle x+60 = 2y-120$

    $\displaystyle x = 2y-180$


    $\displaystyle \frac{x - 100}{y + 100} = \frac{1}{3}$

    $\displaystyle 3x-300 = y+100$

    substitute $\displaystyle 2y-180$ for $\displaystyle x$ ...

    $\displaystyle 3(2y-180)-300 = y+100$

    solve for y , then determine x
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  5. #5
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    I got the x = 2y -180, just didn't what to do next.

    Thanks.
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