2022 MMATHS Individual Round Problems/Problem 1

Problem

Suppose that $a+b = 20, b+c = 22,$ and $a+c = 2022$. Compute $\frac {a-b}{c-a}$.

Solution 1

We solve everything in terms of $a$. $b = 20 - a$ and $c = 2022 - a$. Therefore, $20-a + 2022-a = 22$. Solving for $a$, we get that $a$ = 1010. Since $c = 2022-a, c = 1012$. Since $b = 20-a, b = -990$. Computing $\frac {1010-(-990)}{1012-1010}$ gives us the answer of $\boxed {1000}$.

~Arcticturn