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Math Help - challenging ratio question

  1. #1
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    challenging ratio question

    Dear sir,
    I would be most grateful if someone can help me to solve the below question.
    Thanks

    There are 42 fruits in each of the 2 boxes, box A and box B. The ratio of the number of apples in box A to the number of apples in box B was 3:4. The ratio of the number of oranges in box A to the number of oranges in box B was 4:3. There were 56 apples altogether in both boxes. What is the ratio of the apples in box A to the number of oranges in box B?
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  2. #2
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    Re: challenging ratio question

    Quote Originally Posted by kingman View Post
    Dear sir,
    I would be most grateful if someone can help me to solve the below question.
    Thanks

    There are 42 fruits in each of the 2 boxes, box A and box B. The ratio of the number of apples in box A to the number of apples in box B was 3:4. The ratio of the number of oranges in box A to the number of oranges in box B was 4:3. There were 56 apples altogether in both boxes. What is the ratio of the apples in box A to the number of oranges in box B?
    1. Let x denote the number of apples in box A and y the number of apples in box B. Then the number of oranges in A is 42-x and in B 42-y.

    2. You'll get a system of equations:

    \left|\begin{array}{rcl}\frac xy &=& \frac34 \\ \frac{42-x}{42-y}&=&\frac43 \\ x+y&=&56 \end{array}\right.

    3. Solve for x and y. Afterwards determine the ration \frac x{42-y}.

    By the way: Are you sure that the wording of the question is correct?
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  3. #3
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    Re: challenging ratio question

    Thanls for the reply but I cannot read any equation on the solution and the answer is 1:1
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