Solving the marbles Question by Algebra.

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This is one way of working this out using Algebra

Let the number of marbles that Andrew has be A

Let the number of marbles that Billy has be B

If Andrew gives away one of his marbles he is left with A - 1 marbles. If Billy is given a marble he has B+1 marbles.

They both have the same number of marbles so A - 1 = B+1

or A = B+2 (equation I)

If Billy gives one of his marbles to Andrew then Billy has B - 1 marbles and Andrew has A+1 marbles

We are told that Andrew then has twice as many marbles as Billy so

A+1 = 2(B - 1)

or A+1 = 2B -2

or A= 2B -3

or 2B - 3 = A (equation II)

If we put equation I and equation II together we have

2B - 3 = A = B+ 2

2B - 3 = B + 2

2B = B + 5

B=5 so Billy starts with 5 marbles.

Now if we look at equation 1 A=B+2

Then A = 5 + 2 = 7 so Andrew starts with 7 marbles.

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