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Bob puts some beads into 3 jars A B C. The ratio of the number of beads in jar A to jar B is 2 to 3.
The ratio of beads in B to C is 2 to 1. If Bob transfers
An equal number of beads from B to A and C he will have an equal number of beads in A and B and
the total number of beads in C will increase to 297. What is the total number in all 3 jars.
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Let B = 6x. Then A = 4x and C = 3x.
The total beads is 6x + 4x + 3x = 13x.
After transfering beads, we have 6x-2y in B; 4x+y in A and 3x+y in C.
THEREFORE
3x + y = 297 (1)
6x - 2y = 4x + y (2)
From equation (2), we have
6x - 4x = 2y + y
or
2x = 3y. (3)
Multiply equation (1) by 3 (both sides) to get
9x + 3y = 297*3 (4)
Replace here 3y by 2x, based on (3). Then
9x + 2x = 297*3
11x = 891
x = 891/11 = 81.
ANSWER. The total beads is 81*13 = 1053.
Solved.
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