Question Video: Creating Quadratic Equations in More Than One Variable Mathematics • 9th Grade

Video Transcript

Two siblings are three years apart in age. Write an equation for 𝑃, the product of their ages, in terms of 𝑎, the age of the youngest sibling.

So, we’re told in this question to use the letter 𝑎 to represent the age of the younger sibling. We now want to find an expression in terms of 𝑎 for the age of the older sibling. Well, we’re told that the siblings are three years apart in age. So, the older sibling is three years older than the younger. An expression for the age of the older sibling is, therefore, 𝑎 plus three. The product of their ages means we need to multiply them together. So, we take our two expressions of 𝑎 and 𝑎 plus three and multiply them.

This is a quadratic equation. Because if we were to distribute the parentheses, we have 𝑎 multiplied by 𝑎 giving 𝑎 squared and 𝑎 multiplied by three giving three 𝑎. Either of these two forms would be acceptable for the answer, but we’ll give our answer as 𝑃 equals 𝑎 multiplied by 𝑎 plus three.