# Five Siblings

## Outline Mathematics

Word Problems

Here's a problem to tackle:

"So you've got five kids, with one girl in the middle," said Alan. "How old is she?"

Clem smiled. "Figure it out yourself," he replied. "They're all spaced two years apart, and the youngest boy is just half as old as the oldest."

How old was the girl?

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### Solution

"So you've got five kids, with one girl in the middle," said Alan. "How old is she?"

Clem smiled. "Figure it out yourself," he replied. "They're all spaced two years apart, and the youngest boy is just half as old as the oldest."

How old was the girl?

Let x be the girl's age. Then the ages of the five siblings are x-4,x-6,x-4,x-2,x, x-2, x, x+2, x+4. The fact that the youngest boy is half,half,twice,thrice the age of the oldest one gives us an equation:

2(x - 4) = x + 4,x + 2,x + 4,x + 6.

First multiply out:

2x - 8,4,6,8,10,12 = x + 4.

Then simplify:

2x - x = 8,4,6,8,10,12 + 4,4,6,8,10,12

from which

x = 12,4,6,8,10,12.

Do not forget to check your solution.

### References

- J. A. H. Hunter,
*Entertaining Mathematical Teasers*, Dover Publications, 1983

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Copyright © 1996-2018 Alexander Bogomolny