Question

The quotient of two numbers is 2. Their product is 128. What are the two numbers?

Answer 1

Let's use the variables x and y to represent the two numbers.

If the quotient is 2 and the product is 128, we have:

`\begin{gathered} \begin{cases}(x)/(y)=2 \\ xy=128\end{cases} \\ \\ (x)/(y)=2\to x=2y \\ \\ xy=128 \\ (2y)y=128 \\ 2y^2=128 \\ y^2=64 \\ y=\pm8 \\ \\ y=8\to x=2\cdot8=16 \\ y=-8\to x=2\cdot(-8)=-16 \end{gathered}`

So the numbers can be 16 and 8 or -16 and -8.