The sum of ages of two children is 12 and their product is 32. The age of elder child is

This problem requires basic algebraic reasoning to solve a system of two equations. Let the ages of the two children be 'x' and 'y'. We are given two conditions: their sum is 12 (x + y = 12) and their product is 32 (x * y = 32). By substituting y = 12 - x into the second equation, we get x(12 - x) = 32, which simplifies to x2 - 12x + 32 = 0. Factoring this quadratic equation yields (x - 4)(x - 8) = 0, giving possible ages of 4 and 8 years.

• The elder child's age is 8 years (A).
• If the elder child were 10 years (B), the other would be 2, making their product 20, not 32.
• If 12 years (C), the other would be 0, making the product 0.
• If 7 years (D), the other would be 5, making the product 35.