A and B shared some beads.

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Question from Nicholas, a student:

A and B shared some beads. A gave 1/3 to B, B will have 70 more than A. If A gave 1/5 to B, B would have 10 more than A. A have how many at first ?

Nicolas,

I can get you started.

Suppose A has x beads and B has y beads. If A gives one-third of her beads then she will be left with two-thirds of her brads, 2/3 x, and B will have y + 1/3 x beads. You are told that if this happens B will have 70 more beads than A, that is

y + 1/3 x - 2/3 x = 70

y = 1/3 x = 70.

Use the statement "If A gave 1/5 to B, B would have 10 more than A." to develop a second equation in x and y and then solve this pair of equations.

Penny

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