Question 529934: the sum of present ages of a father and his son is 80 years.when the fathers age was equal to the present age of the son,the sum of their ages was 40 years.find their present ages
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let F represent the present age of the father and let S represent the present age of the son.
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The problem tells you that the sum of the present ages of the father and son is 80 years. Writing this in equation form results in:
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F + S = 80
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A little trickier is getting a second equation. You are told that "when the father's age was equal to the present age of the son ..." That means that when the father's age was S. Ask yourself how many years ago was that. The answer to that question is to subtract the son's present age S from the father's present age F. So it was F - S years ago. Now find the son's age that many years ago by subtracting the number of years ago from the son's present age. In other words:
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S - (F - S)
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Because the parentheses are preceded by a minus sign, you can remove the parentheses by changing the signs of the terms inside the parentheses to get:
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S - F + S = 2S - F
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So at the time the father's age was S, the son's age was 2S - F. The problem tells you that the sum of these two ages was 40. When you add these two ages and set the sum equal to 40 you get the equation:
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S + 2S - F = 40
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Add the terms containing S on the left side and this equation becomes:
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3S - F = 40
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So we now have the following two equations to solve simultaneously:
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F + S = 80
3S - F = 40
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Let's solve these equations by eliminating one of the variables. In the second (or bottom) equation transpose the two terms on the left side to get:
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-F + 3S = 40
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Now write the two equations again:
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F + S = 80
-F + 3S = 40
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If we add these two equations vertically, the F and the -F will cancel each other. The S will add to the 3S to get 4S and the 80 will add to the 40 to result in 120. So by adding the two equations we get:
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4S = 120
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Solve for S by dividing both sides by 4 and the result is:
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S = 120/4 = 30
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We now know that S, the son's present age is 30. Since adding the son's present age to the father's present age equals 80:
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F + 30 = 80
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Solve for F by subtracting 30 from both sides of this equation to get:
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F = 50
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So the father's present age is 50 and the son's present age is 30.
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20 years ago when the father's age was 30 (the same as the son's present age) the son was 10 years old, and the sum of their two ages 20 years ago was:
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30 + 10 = 40
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This checks out and shows that everything checks out.
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Hope this helps you to understand the problem.
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