Art of Problem Solving
AoPS Online
Math texts, online classes, and more
for students in grades 5-12.
Visit AoPS Online ‚
Books for Grades 5-12 Online Courses
Beast Academy
Engaging math books and online learning
for students ages 6-13.
Visit Beast Academy ‚
Books for Ages 6-13 Beast Academy Online
AoPS Academy
Small live classes for advanced math
and language arts learners in grades 2-12.
Visit AoPS Academy ‚
Find a Physical Campus Visit the Virtual Campus

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

(Created page with "=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>.")
 
(→‎Problem)
Line 2: Line 2:
  
 
Suppose that <math>a+b = 20, b+c = 22,</math> and <math>a+c = 2022</math>. Compute <math>\frac {a-b}{c-a}</math>.
 
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

Revision as of 20:54, 18 December 2022

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

Retrieved from "https://artofproblemsolving.com/wiki/index.php?title=2022_MMATHS_Problems/Problem_1&oldid=184214"