Difference between revisions of "2022 MMATHS Problems/Problem 1"

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-=Problem=
-Suppose that <math>a+b = 20, b+c = 22,</math> and <math>a+c = 2022</math>. Compute <math>\frac {a-b}{c-a}</math>.
-==Solution 1==
-We solve everything in terms of <math>a</math>. <math>b = 20 - a</math> and <math>c = 2022 - a</math>. Therefore, <math>20-a + 2022-a = 22</math>. Solving for <math>a</math>, we get that <math>a</math> = 1010. Since <math>c = 2022-a, c = 1012</math>. Since <math>b = 20-a, b = -990</math>. Computing <math>\frac {1010-(-990)}{1012-1010}</math> gives us the answer of <math>\boxed {1000}</math>.
-~Arcticturn

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