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

SOLUTION

Let the two integers be x and y.

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

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

The quotient of x and y is 5, that is

$\begin{gathered} x\div y=5 \\ \frac{x}{y}=5\ldots\ldots\ldots\ldots\text{.}\mathrm{}\text{equation 2} \end{gathered}$

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

$\begin{gathered} \frac{x}{y}=5 \\ \text{cross multiplying } \\ 5\times y=x \\ x=5y \end{gathered}$

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

$\begin{gathered} xy=80 \\ 5y\times y=80 \\ 5y^2=80 \\ \text{dividing by 5} \\ y^2=\frac{80}{5} \\ y^2=16 \\ \text{take square root of both sides } \\ \sqrt[]{y^2}=\sqrt[]{16} \\ \text{square cancels root} \\ y=4 \end{gathered}$

Now substitute y for 4 into any of the equations.

Let us use equation 1 again, we have

$\begin{gathered} xy=80 \\ x\times4=80 \\ 4x=80 \\ x=\frac{80}{4} \\ x=20 \end{gathered}$

Hence the answer is 4, 20