Question 114144
Here's your work. You had a very good start on the problem:
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let P be Perla's age  and M be Marilou's age <=== good. Your selection of P for Perla's age 
and M for Marilou's age helps you to identify the ages better than X and Y or some other letters.

a) P = 5M <=== this is correct
b) P+10 = 3M <=== your mistake is here.
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In 10 years, Perla's age will be P + 10, just as you showed on the left side. But Marilou
will have aged 10 years also, so her age at that time will be M + 10. So three times her age
at that time would make the equation become:
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P + 10 = 3(M + 10)
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and you can simplify this by multiplying out the right side to get:
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P + 10 = 3M + 30
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Get rid of the 10 on the right side by subtracting 10 from both sides to get:
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P = 3M + 20
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But up in step a) you found that P = 5M. So you can substitute 5M for P and the equation is:
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5M = 3M + 20
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Get rid of the 3M on the right side by subtracting 3M from both sides. This makes the
equation reduce to:
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2M = 20
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and solve for M (which is Marilou's present age) by dividing both sides by 2 to get:
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M = 10
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So Marilou is presently 10 years old. 
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and since Perla is 5 times older than Marilou, Perla is 5*10 or 50 years old.
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Ten years from now Perla will be 60 years old. And 10 years from now Marilou will be
20 years old. And sure enough, in 10 years Perla's age (60) will be three times Marilou's 
age (20). So this answer checks.
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Your thinking was right on ... you just made a very common error ... you forgot that Marilou's 
age went up by 10 years also. That's an easy mistake to make, but now you should have the idea.
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Keep up the good work ... you've got the basic idea of how to do these problems and with
a little practice you'll be good at it.
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Hope this helps.
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