ratio of apples

• September 14th 2010, 05:50 PM
kingman
ratio of apples
Dear Sir
I would be grateful if you can help me to solve the the below questions
thanks
Kingsman

At the party, each child had either 1 apple or 2 apples. If the ratio of the number of children to the number of apples was 5: 8, what fraction of the children had 2 apples each?
• September 14th 2010, 06:16 PM
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Quote:

Originally Posted by kingman
Dear Sir
I would be grateful if you can help me to solve the the below questions
thanks
Kingsman

At the party, each child had either 1 apple or 2 apples. If the ratio of the number of children to the number of apples was 5: 8, what fraction of the children had 2 apples each?

2 + 2 + 2 + 1 + 1 = 8
• September 15th 2010, 05:19 AM
kingman
Dear Sir,
Can you show me how to do this question algebraically.
Thanks
• September 15th 2010, 05:43 AM
Soroban
Hello, kingman!

Quote:

At the party, each child had either 1 apple or 2 apples.
If the ratio of the number of children to the number of apples was 5: 8,
what fraction of the children had 2 apples each?

Let $\,A$ = number of children with 1 apple.
Let $\,B$ = number of children with 2 apples.

Then there were: . $A+B$ children.

And there were: . $A + 2B$ apples.

. . We want the fraction: . $\dfrac{B}{A+B}$

We are told that: . $\dfrac{\text{children}}{\text{apples}} \:=\:\dfrac{5}{8}$

. . . .So we have: . $\dfrac{A+B}{A+2B} \:=\:\dfrac{5}{8}
$

which simplifies to: . . . $\dfrac{A}{B} \;=\;\dfrac{2}{3}$

Add 1 to both sides: . $\dfrac{A}{B} + 1 \;=\;\dfrac{2}{3} + 1 \quad\Rightarrow\quad \dfrac{A+B}{B} \;=\;\dfrac{5}{3}$

. . Therefore: . $\dfrac{B}{A+B} \;=\;\dfrac{3}{5}$
• September 15th 2010, 05:59 AM
kingman
Dear Soroban.
You are a fantastic problem solver and I love your approach to the problem very much.Crystal Clear!
Thousand Thanks
Kingman
• September 15th 2010, 06:26 PM
kingman
Dear Sir,
Can this problem be solved by looking at the remainder when the number of apples ( 8x ) is divided by the number of children ( 5x)
Thanks
Kingman