Question 105578
Let the age of Rex's father be F.
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Then Rex's age (30 years younger than his father) is F - 30.
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Rex's mother is 3 times as old as Rex. So her age is 3 times Rex's age or 3(F - 30).
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Rex's father's age (which is F) is two years more than his mother's age (which is 3(F - 30).
So if you take 2 years from his father's age, the result will equal his mother's age. In
equation form this is:
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F - 2 = 3(F - 30)
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Multiply out the right side and you have:
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F - 2 = 3F - 90
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Get rid of the 2 on the left side by adding 2 to both sides:
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F = 3F - 88
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Eliminate the 3F on the left side by subtracting 3F from both sides to make the equation
become:
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-2F = -88
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Solve for F by dividing both sides by -2 and you have:
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F = -88/-2 = 44
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So Rex's father is 44 years old. Since Rex is 30 years younger than that, Rex is 44 - 30 or 14
years old. And since Rex's mothers age is 3 times Rex's age, his mother is 3 times 14 or
42 years old. Notice that Rex's father is two years older than Rex's mother, so the problem
checks.
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In summary ... Rex's age is 14.
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Hope this helps you to understand the problem.
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