Question 40339
Good Question. I'm guessing you meant 30/(10+y) = 20/(10-y).
Anyway, our first aim is to get rid of the denominators because those don't help a lot when solving equations. So we can first multiply both sides by (10+y) and then multiply both sides by (10-y).
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{{{(10+y)*(30/(10+y)) = (20/(10-y))*(10+y)}}} (we multiply both sides by 10+y)
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{{{30 = (20*(10+y))/(10-y)}}}
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{{{(10-y)*30 = 20*(10+y)}}} (we multiply both sides by 10-y)
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We can factor this out:
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{{{300-30y = 200+20y}}}
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{{{100 = 50y}}} (subtract 200 from both sides, and add 30y to both sides)
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{{{y = 2}}} (the final answer)