Question

The sum of two numbers is 118. if four times the smallest numbers is subtracted from the largest number the result is 18. Find the two numbers.

Answer 1

Let's say the two numbers are "a" and "b"
"a" being the smaller one, and "b" the larger one

so, their sum is 118, or a + b = 118

if 4 times the smallest, or 4*a or 4a
is subtracted from the largest, "b",  so  b - 4a
equals 18, so b - 4a = 18

thus    $\bf \begin{cases} a+b=118\implies \boxed{b}=118-a\\ b-4a=18\\ ----------\\ \left( \boxed{118-a} \right)-4a=18 \end{cases}$

solve for "a", to find the smaller one

what's b?   well, b = 118 - a