# challenging ratio question

• Jun 29th 2011, 07:41 AM
kingman
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?
• Jun 29th 2011, 09:06 AM
earboth
Re: challenging ratio question
Quote:

Originally Posted by kingman
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?
• Jun 29th 2011, 06:24 PM
kingman
Re: challenging ratio question
Thanls for the reply but I cannot read any equation on the solution and the answer is 1:1