Question

There are four children of different integers under 18. The product of their ages is 882. What is the sum of their ages?

Answer 1

I am thinking the answer is 49

Answer 2

Answer: The sum of age of four children is 31.

Explanation:

It is given that there are four children of different integers under 18. The product of their ages is 882.

Since the product of ages is equal to 882, therefore the ages of children must be the factor of 882.

The factors of 882 are 1, 2, 3, 3, 7 and 7.

$882=1\times 2\times 3\times 3\times 7\times 7$

Since the age of four children are different, therefore we use these factors to find the age of children.

Let age of one child is 7, then the age of other child is multiple of three.

It should be multiple of 2 because $7\times 3=21$ which is more than 18. S the age of second child is 14.

Now we have 1, 3 and 3. Two factors are same. So the age of third child must be multiplication of common factor 3 and 3. Thus, the age of third child is 9.

The remaining factor is 1, so the age o fourth child is 1.

The ages of childers ae 1, 7, 9 and 14.

Sum of the ages is,

$1+7+9+14=31$

Therefore, the sum of their age is 31.