Question

The product of two integers is eighty,their quotient is five.Write both integers in numerical order and separated by a comma,no spaces.

Answer 1

Let the two integers be x and y.

Now, the product of x and y, is 80, that is

`\begin{gathered} x* y=80 \\ xy=80\ldots\ldots\text{.equation 1} \end{gathered}`

The quotient of x and y is 5, that is

`\begin{gathered} x/ y=5 \\ (x)/(y)=5\ldots\ldots\ldots\ldots\text{.}\mathrm{}\text{equation 2} \end{gathered}`

From equation 2, make x, the subject, we have

`\begin{gathered} (x)/(y)=5 \\ \text{cross multiplying } \\ 5* y=x \\ x=5y \end{gathered}`

Now substitute the x for 5y into equation 1, we have

`\begin{gathered} xy=80 \\ 5y* y=80 \\ 5y^2=80 \\ \text{dividing by 5} \\ y^2=(80)/(5) \\ y^2=16 \\ \text{take square root of both sides } \\ \sqrt[]{y^2}=\sqrt[]{16} \\ \text{square cancels root} \\ y=4 \end{gathered}`

Now substitute y for 4 into any of the equations.

Let us use equation 1 again, we have

`\begin{gathered} xy=80 \\ x*4=80 \\ 4x=80 \\ x=(80)/(4) \\ x=20 \end{gathered}`

Hence the answer is 4, 20