SOLUTION: Two boys have 252 marbles between them. One arranges them in heaps of 6 each, the other in heaps of 9 each,and there are 34 heaps in all.how many marbles has each boy?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Two boys have 252 marbles between them. One arranges them in heaps of 6 each, the other in heaps of 9 each,and there are 34 heaps in all.how many marbles has each boy?      Log On


   

Question 665700: Two boys have 252 marbles between them. One arranges them in heaps of 6 each, the other in heaps of 9 each,and there are 34 heaps in all.how many marbles has each boy?
Found 2 solutions by danica11, MathTherapy:
Answer by danica11(1) About Me  (Show Source):
Answer by MathTherapy(10552) About Me  (Show Source):
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Two boys have 252 marbles between them. One arranges them in heaps of 6 each, the other in heaps of 9 each,and there are 34 heaps in all.how many marbles has each boy?

Let the amount of heaps boy 1 has be H%5B1%5D, and amount of heaps boy 2 has, H%5B2%5D
Since there are 34 heaps, then H%5B1%5D+%2B+H%5B2%5D+=+34 ------ eq (i)
Also, 6H%5B1%5D+%2B+9H%5B2%5D+=+252 ------ 3%282H%5B1%5D+%2B+3H%5B2%5D%29+=+3%2884%29 ----- 2H%5B1%5D+%2B+3H%5B2%5D+=+84 ------- eq (ii)
-+2H%5B1%5D+-+2H%5B2%5D+=+-+68 ----- Multiplying eq (i) by – 2 ------ eq (iii)
H%5B2%5D+=+16 ------ Adding eqs (iii) & (ii)
H%5B2%5D, or heaps that boy 2 has = highlight%2816%29

H%5B1%5D+%2B+16+=+34 ------- Substituting 16 for H%5B2%5D in eq (i)
H%5B1%5D+=+34+-+16
H%5B1%5D, or heaps that boy 1 has = highlight%2818%29

Since boy 1 has 18 heaps, with 6 marbles in each heap, then boy 1 has 18 * 6, or highlight_green%28108%29 marbles

Since boy 2 has 16 heaps and 9 marbles in each heap, then boy 2 has 16 * 9, or highlight_green%28144%29 marbles

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