Question

The sum of two whole numbers is 18 and their product is 45, the numbers are ______.

Options

• 15 and 3

• – 15 and – 3

• – 15 and 3

• 15 and – 3

Answer 1

The sum of two whole numbers is 18 and their product is 45, the numbers are 15 and 3.

Explanation:

Let the two whole numbers are x and 18 – x and their product is 45.

∴ x(18 – x) = 45

`\implies` 18x – x² = 45

`\implies` x² – 18x + 45 = 0

`\implies` x² – 3x – 15x + 45 = 0

`\implies` x(x – 3) – 15(x – 3) = 0

`\implies` (x – 3)(x – 15) = 0

Either x – 3 = 0 or x – 15 = 0

`\implies` x = 3 or x = 15

`\implies` x = 3 or 15