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?
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Kaden Adam John
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
Hence John gave away 9×3 = 27 marbles
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. CHECK Kaden Adam John Gave 6 12 27 (6:12:27 = 2:4:9) Left 8=2+6 16 32 (sum = 56)