```Question 116313
Let R represent Renato's present age. Let D represent Doming's present age.
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Since Renato is 3 years younger that Doming, this means that if we add 3 years to Renato's
age, the answer will equal Doming's age. In equation form this is:
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R + 3 = D
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6 years ago, how old was Renato? The answer to that is R - 6. And 6 years ago, how old was
Doming? The answer to that is D - 6. The problem tells you that at that time Renato's age
was two-thirds of Doming's age. So we can say:
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R - 6 = (2/3)*(D - 6)
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But we had an earlier equation that said R + 3 equals D. So in this equation we can substitute
R + 3 for D and get:
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R - 6 = (2/3)*(R + 3 - 6)
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Inside the second set of parentheses we can combine the +3 and the -6 to get -3. This makes
the equation become:
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R - 6 = (2/3)*(R - 3)
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Multiply out the right side and get:
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R - 6 = (2/3)R - 2
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You can get rid of the fraction by multiplying the entire equation (both sides and all terms) by
3 to get:
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3R - 18 = 2R - 6
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Get rid of the -18 on the left side by adding 18 to both sides and you have:
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3R = 2R + 12
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Get rid of the 2R on the right side by subtracting 2R from both sides and you have:
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R = 12
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So we can tell that Renato's present age is 12. And since Renato is 3 years younger than
Doming, that means that Doming is 15 years old.
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Six years ago Renato was 12 - 6 or 6 years old. And six years ago Doming was 15 - 6 = 9 years old.
Renato's age at that time (6) was two-thirds of Doming's age (9), so that checks also.
The answers check ... Renato is presently 12 and Doming is presently 15.
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Hope this helps you to understand the problem.
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