Question

the sum of 2 numbers is 96. the larger number is 9 less than 4 times the smaller. find boh nmbers.

Answer 1

The sum of 2 numbers is 96, this can be expressed as

$x+y=96$

The larger number is 9 less than 4 times the smaller, this can be expressed as

$x=4y-9$

Now, we replace the second equation in the first one

$\begin{gathered} 4y-9+y=96 \\ 5y=96+9 \\ y=\frac{105}{5} \\ y=21 \end{gathered}$

We use this number to find x.

$x=4\cdot21-9=84-9=75$

Hence, the numbers are 75 and 21.