2022 MMATHS 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

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2022 MMATHS Problems/Problem 1

Problem

Solution 1