SOLUTION: Hi 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

Question 1188031: Hi
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.
Thanks

Answer by ikleyn(52788) (Show Source): You can put this solution on YOUR website!
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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.
~~~~~~~~~~~~~~

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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