Chad W. answered • 01/27/18

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I think I understand. Steve and Laura initially had crayons in a ratio of 7:2. After Steve gives Laura 15 of his crayons, the both have equal amounts. Then, we want to know their final amounts? Or their initial amounts? I guess I will just answer both.

Let's write what we know in algebraic language. I will use "/" to mean division. I will use S for Steve's initial amount and L for Laura's initial amount.

S / L = 7 / 2

S - 15 = L + 15

I would use substitution. So, first solve the second equation for S in terms of L.

S = L + 30

Now, substitute into the first equation.

(L + 30) / L = 7 / 2

Multiply both sides by 2*L.

2*(L + 30) = 7 * L

Distribute.

2L + 60 = 7L

Subtract 2L from both sides.

60 = 5L

Divide both sides by 5.

12 = L

Laura started with 12 crayons. Steve started with 30 more (Remember S = L + 30), so Steve began with 42 crayon. Indeed, we should check that 42/12 = 7/2.

After the transfer of crayons, they each would have 27 crayons.