Two cash registers of a store had a combined total of $300. When the manager tranferred $15 from one register to the other, each had the same amount. How much did each register have before?

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so the first equation is x+y=300 the next equation is x+15=y-15 because you take 15 off of one register and add it to the other; the simplify the latter, to get x+30=y substitute that in for the first equation to get: x+x+30=300--->2x+30=300-->2x=270=135 so one register has 135 and the other has 30 more because x+30=y  so the other has 165 and 165+135=300 so it works. final answer is 135 and 165