 # Question

The ratio of the number of marbles Kaden, Adam, and John gave away was 2:4:9. The number of marbles Kaden have away was 2 fewer than the number of marbles he had left. Adam had 1/2 as many marbles left as John. Kaden had 1/2 as many marbles left as Adam. They had a total of 56 marbles left. How many marbles did John give away?

Gave away                         2u                                        4u                                                  9u

Marbles left                   2u+2                             2(2u+2)=4u+4                            2(4u+4)=8u+8

( give away 2 fewer than left)  (K  1/2 as many left as A)      (A 1/2 as many left as J)

2u+ 2 + 4u+4 + 8u + 8 = 56

14u =56 -14 = 42

u= 3

Hence John gave away 9×3 = 27 marbles

0 Replies 1 Like

Is there a typo? “The number of marbles Kaden have away was 2 fewer than the number of marbles he had left. ”  I assume it is “gave away”.

```Suppose Kaden had u marbles left. Then Adam had 2u left and John 4u left.
So total left = u + 2u + 4u = 7u = 56 and thus u = 56/7 = 8.

Kaden gave away 8 - 2 = 6 marbles.
John gave away 6 / 2 * 9 = 27 marbles.
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