If the sum of the ages of two children is 12 and their product is 32, which one is the elder?

If the sum of the ages of two children is 12 and their product is 32, which one is the elder?

Explanation

To find the ages, solve the equations:  

Let the ages be x and 12 - x.

The product is x(12 - x) = 32.

Solving x^2 - 12x + 32 = 0 gives x = 4 and x = 8

So, the ages are 4 and 8 years.

The elder child is: 8 years.