2023 CEMC Fermat Problems/Problem 2

Problem

If $3 + x = 5$ and $-3 + y = 5$ , then $x + y$ equals

$\text{ (A) }\ 4 \qquad\text{ (B) }\ 16 \qquad\text{ (C) }\ 6 \qquad\text{ (D) }\ 12 \qquad\text{ (E) }\ 10$

We can solve the first equation for $x$ , solve the second equation for $y$ , and then add $x$ and $y$ together.

$3 + x = 5$

$x = 5 - 3 = 2$

$-3 + y = 5$

$y = 5 + 3 = 8$

$x + y = 2 + 8 = \boxed {\textbf {(E) } 10}$

~anabel.disher

Both equations have $x$ and $y$ with a coefficient of $1$ , so we can just add them together:

$3 + x - 3 + y = 5 + 5$

Simplifying both sides, we get:

$x + y = \boxed {\textbf {(E) } 10}$

~anabel.disher