Question 87803: Herny's father is now twice as old as Henry. Sixteen years ago, he was four times as old. How old is each now??
1 solution
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Let F represent the current age of Henry's father. And Let H represent Henry's current age.
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Currently the father is twice as old as Henry. Therefore, if you double Henry's current
age, the result equals the father's age. In equation form this is:
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F = 2*H
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Sixteen years ago, the father's age was his current age less 16 which is F - 16. The same
with Henry. Sixteen years ago Henry was his current age less 16 or H - 16. And at that time
the father's age (F - 16) was equal to 4 times Henry's age [4 times (H - 16)]. In equation
form this is:
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F - 16 = 4*(H - 16)
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Simplify this by multiplying out the right side to get:
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F - 16 = 4H - 64
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Then get rid of the -16 on the left side by adding 16 to both sides. When you add 16
to both sides you get:
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F = 4H - 48
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Now from the first equation we wrote, F = 2H. So we can substitute 2H in place of F
in the equation and with this substitution the equation
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F = 4H - 48
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becomes:
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2H = 4H - 48
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Next let's get rid of the 4H on the right side by subtracting 4H from both sides.
When you subtract 4H from both sides, the equation becomes:
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-2H = -48
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Divide both sides by -2 which is the multiplier of H and you get:
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H = -48/-2 = 24
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This tells us that Henry is currently 24 years old. And since we know that his father
is presently twice as old as he is, Henry's father must currently be 48 years old.
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Let's check that. Sixteen years ago, Henry's father was 48 - 16 = 32 years old and also
16 years ago, Henry was 24 - 16 = 8 years old. So 16 years ago the father's age (32) was
4 times Henry's age (8). That works! So the answer to the problem is that Henry is currently
24 years old and his father is currently 48 years old.
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Hope this helps you to understand the problem and a process that you can use to solve it.
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