SOLUTION: Hi The ratio of apples alicia Ben and Don has 3 to 8 to 4 respectively. When Ben gave 21 apples to alicia and Don all of them had the same number in the end. How many apples did

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Question 1206035: Hi
The ratio of apples alicia Ben and Don has 3 to 8 to 4 respectively. When Ben gave 21 apples to alicia and Don all of them had the same number in the end. How many apples did Ben have at first.
Thanks
Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Given the ratio 3:8:4 initially, let the numbers of apples each of them had be 3x, 8x, and 4x. The total number of apples is then 3x+8x+4x = 15x.

In the end, each of them had the same number; so in the end the number each of them had was 15x/3 = 5x.

The number of apples Ben started with was 8x; the number he ended with was 5x; so the number he gave away was 3x.

The number he gave away was 21, so 3x = 21 and x = 7.

The number Ben started with was 8x = 8*7 = 56.

ANSWER: 56

Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Alicia       3x           3x+(21-n)
Ben          8x           8x-21
Don          4x           4x+n

system%283x-n%2B21=8x-21%2C8x-21=4x%2Bn%29
-
system%28-5x-n=-42%2C4x-n=21%29

system%285x%2Bn=42%2C4x-n=21%29

ADD correspondings....
9x=63
highlight_green%28x=7%29

Ben initially had 8%2A7=highlight%2856%29 apples.