find the total number of marbles in the bag.

Question

Paul has a bag of marbles. He divided the marbles into three boxes, A, B and C. The total number of marbles in box A and B as compared to the marbles in box C is in the ratio of 7:5, and the total number of marbles in box B and C as compared to the marbles in box. A is in the ratio of 13:8.

Given that there are 34 marbles in box B,

Answer 1

(A+B)/C = 7/5=

5A + 5B = 7C

multiply by 8

40A + 40B = 56C

(B+C)/A = 13/8

8B + 8C = 13A

multiply by 7

56B + 56C = 91A

91A - 56B = 56C

subtract to eliminate 1 variable, eliminating C

40A +40B= 56C

leaving

51A -96B = 0

A = 96(34)/51 = 64 marbles in box A

8C = 13(64)-272 = 560/8 = 70 marbles in box C

B = 34 marbles in box B

Total marbles in the bag = 64+34+70 = 168

64+34)/70 = 98/70 = 7/5

70+34)/64 =104/64 = 13/8