Question

The sum of two numbers is 64. If four times the smaller number is subtracted from the larger​ number, the result is 4. Find the two numbers

Answer 1

`\huge\boxed{52,\ 12}`

Explanation:

`x,\ y-\text{the numbers}\ (x<y)\\\\\text{first equation}:x+y=64\\\\\text{second equation}:x-4y=4\\\\\underline{-\left\{\begin{array}{ccc}x+y=64\\x-4y=4\end{array}\right }\qquad\text{subtract both sides of the equations}\\x-x+y-(-4y)=64-4\\y+4y=60\\5y=60\qquad\text{divide both sides by 5}\\\boxed{y=12}\\\\\text{Substitute it to the first equation:}\\x+12=64\qquad\text{subtract 12 from both sides}\\\boxed{x=52}`