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Let Andy have u marbles at the beginning.

So Ben have u + 15 marbles at the beginning.

Since the ratio of Andy’s marbles to Ben’s marbles was 5:8, it means

u/u+15 = 5/8
8u = 5(u + 15)
8u = 5u + 75
3u = 75
u = 25

a) So together, they must have u + (u + 15) = 25 + 25 + 15 = 65 marbles #

b) Since the ratio is 3 : 2 after Ben lost some marbles to Andy,
Ben must have now 2/5 of 65 marbles = 26 marbles

Originally, Ben had  u + 15 marbles = 25 + 15 = 40 marbles

So Ben lost 40 – 26 = 14 marbles #

1 Reply 1 Like ✔Accepted Answer

Oops.  Corrected my syntax error.  Thank you, @Mr.Tan!

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a. We can represent 5:8 as above. So clearly 3u = 15 and u = 5.
In total they had (5+8) x 5 = 13 x 5 = 65 marbles altogether.

b. If their final ratio is 3:2, that means each unit in 65/(3+2) = 13.
So Andy now has 3x13 = 39 and Ben has 2x13 = 26.
Ben originally had 8u = 8x5 = 40. So Ben lost 40 - 26 = 14 marbles.

(if you find this useful, please accept answer; thanks!)
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