### Brain Teasers

# The Three Children of Mr. and Mrs. Jones

Mr. and Mrs. Jones have three children, all under the age of 20, but none with the same age.

Last year, the product of the three ages was 224.

This year the product of the three ages is 360

What are the children's ages now?

Last year, the product of the three ages was 224.

This year the product of the three ages is 360

What are the children's ages now?

### Hint

Don't waste your time trying to set up an equation. All the ages are integers, go from there.### Answer

5, 8, and 9The prime factorization of 224 is 2^5*7.

Using this, the possible sets of three ages of which the product is 224 are:

2, 7, 16

4, 7, 8

2, 8, 14

Now to find out which one of these sets was their ages a year ago, add 1 to each number and multiply:

3*8*17

5*8*9

3*9*15

The only set which multiplies to 360 is the 5, 8, and 9 set, meaning that these are the children's current ages.

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