Question

one number is 4 times a second number and their sum is 80. find the two numbers

Answer 1

In order to find the two numbers mentioned we need to name them as variables, then,

$\begin{gathered} number\text{ 1: }x \\ number\text{ 2: }y \end{gathered}$

then, translate both sentences into equations,

one number is 4 times a second number:

$x=4y$

the sum of the numbers is 80:

$x+y=80$

then, replace the first equation into the second:

$\begin{gathered} 4y+y=80 \\ solve\text{ }for\text{ }y \\ 5y=80 \\ y=\frac{80}{5} \\ y=16 \end{gathered}$

find the value of x

$\begin{gathered} x=4y \\ x=4\times16 \\ x=64 \end{gathered}$

Answer:

The numbers are 16 and 64.