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Math Help - Ratio

  1. #1
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    Question Ratio

    Ratio of two sums of money is 4:3

    if larger sum of money is increased by $40, the ratio becomes 2:1.

    What are sums of money ?

    How to solve this ?


    Solution

    (4/7)*x+(3/7)*y=4:3

    cant understand it....
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  2. #2
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    Re: Ratio

    Quote Originally Posted by haftakhan View Post
    Ratio of two sums of money is 4:3

    if larger sum of money is increased by $40, the ratio becomes 2:1.

    What are sums of money ?

    How to solve this ?


    Solution

    (4/7)*x+(3/7)*y=4:3

    cant understand it....
    Dear haftakhan,

    Let x and y be the sums of money. Take x as the larger sum.

    \frac{x}{y}=\frac{4}{3}

    If larger sum of money is increased by $40, the ratio becomes 2:1.

    Therefore, \frac{x+40}{y}=2

    Solve these two equations and find x and y.
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  3. #3
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    Re: Ratio

    solving this i get x=160 and y=120

    is it correct ?
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  4. #4
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    Re: Ratio

    Quote Originally Posted by haftakhan View Post
    solving this i get x=160 and y=120

    is it correct ?
    No. It is incorrect.
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  5. #5
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    Re: Ratio

    \frac{160}{120}= \frac{40(4)}{40(3)}= \frac{4}{3} so those are in ratio 4:3.

    But adding $40 to $160 give $200.
    \frac{200}{12}= \frac{40(5)}{40(3)}= \frac{5}{3}, or 5:3, not 2:1.
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  6. #6
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    Re: Ratio

    it may be easier to solve the two equations writing them like this:

    3x = 4y
    x+40 = 2y

    one way of doing this, is to write (from the 2nd equation):

    x = 2y - 40.

    now use this in the first equation.
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  7. #7
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    Re: Ratio

    i was about to post the correct answer but the light went off.

    x=80 and y=60
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  8. #8
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    Re: Ratio

    Quote Originally Posted by haftakhan View Post
    i was about to post the correct answer but the light went off.

    x=80 and y=60
    Post #5 shows you how to check this answer for yourself.
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  9. #9
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    Smile Re: Ratio problem

    ratio of two sums = 4 : 3 =  \frac{4}{3} = \frac{4x}{3x} ........... (1)
    When $40 is increased to the larger sum, the ratio is = \frac{4x+40}{3x} = \frac{2}{1}.........(given)
    \therefore 1\times (4x+40) = 2\times{3x}
    =  4x + 40 = 6x
    =  40 = 6x-4x
    =  2x = 40
    = \therefore  x = 20
    By replacing the value of x in the first equation, we get $80 and $60.
    So the sum of $80 and $60 = $140.
    We had $140. Answer.

    I think you have understood this. All the best
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