Question 1105241
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Let 8x be the number of dolls Karen started with and 3x be the number Hannah started with.<br>
(NOTE: When a problem gives you a ratio 8:3 like this, that is nearly always a good way to start on the problem -- letting the two numbers be represented by 8x and 3x.)<br>
After Karen give 15 dolls to Hannah, the number she has left is 8x-15, and the number Hannah now has is 3x+15.  So<br>
{{{8x-15 = 3x+15}}}<br>
Solve using basic algebra....