Question 89775: A man is 41 years old and his son is 9. In how many years will the father be three times as old as his son?
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! You need to add some unknown years to both the man's present age and the boy's present
age. Call that unknown number of years "x".
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In x years, the man will be 41 + x years old and the boy will be 9 + x years old.
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The problem tells you that at that time the man will be three times as old as the boy.
In other words, if you multiply the boy's age by 3, the result will equal the man's age.
In equation form this is:
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41 + x = 3(9 + x)
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Multiply out the right side by multiplying 3 times each of the terms in the parentheses.
When you do that multiplication you get:
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41 + x = 27 + 3x
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To solve this equation, you begin by getting all the terms containing x on one side of
the equation, and then getting all the numbers on the other side. Start by getting rid
of the x on the left side by subtracting x from both sides. When you do that subtraction
you get:
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41 = 27 + 2x
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Now get rid of the 27 on the right side by subtracting 27 from both sides to make the
equation become:
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14 = 2x
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Finally, solve for x by dividing both sides by 2:
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7 = x
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This tells you that in 7 years the man's age should be 3 times the boy's age.
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Check:
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In 7 years the man will be 41 + 7 = 48 years old. And 7 years from now the boy will be
9 + 7 = 16 years old. Will the man's age be 3 times the boy's age? Yes it will. So the
answer of 7 years is correct.
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Hope this helps you to understand this age problem a little better.
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