SOLUTION: The three Smith children have a combined age of 50. The youngest is half as old as the oldest. Ten years ago, the oldest was 7 times as the youngest. How old were the children ten

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Question 1013490: The three Smith children have a combined age of 50. The youngest is half as old as the oldest. Ten years ago, the oldest was 7 times as the youngest. How old were the children ten years ago? (3 answers)

Found 3 solutions by stanbon, fractalier, MathTherapy:
Answer by stanbon(75887)   (Show Source):
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The three Smith children have a combined age of 50. The youngest is half as old as the oldest. Ten years ago, the oldest was 7 times as the youngest. How old were the children ten years ago? (3 answers)
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a + b + c = 50
a = (1/2)c
c-10 = 5(a-10)
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Using the last two equations:
2a-10 = 5a-50
3a = 40
a = 13 1/3 yrs
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Then c = 2a = 26 2/3
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Substitue into the 1st to get:
13 1/3 + b + 26 2/3 = 50
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b + 40 = 50
b = 10 yrs
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Cheers,
Stan H.
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Answer by fractalier(6550)   (Show Source):
You can put this solution on YOUR website!
Let the youngest child be x. The next kids are y and z. We have
x + y + z = 50
x = (1/2)z or z = 2x
z-10 = 7(x-10)
Substituting we have
2x - 10 = 7(x - 10)
2x - 10 = 7x - 70
5x = 60
x = 12 (youngest)
z = 2(12) = 24 (oldest)
y = 50 - 12 - 24 = 14 (middle)

Answer by MathTherapy(10552)   (Show Source):
You can put this solution on YOUR website!

The three Smith children have a combined age of 50. The youngest is half as old as the oldest. Ten years ago, the oldest was 7 times as the youngest. How old were the children ten years ago? (3 answers)

Youngest's:
Middle's:
Oldest's: