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?
Answer
5, 8 and 9
The prime factorization of 224 is 2^57. 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: 3817 589 39*15
The only set which multiplies to 360 is the 5, 8 and 9 set, meaning that these are the children’s current ages.
