Question 399·Medium·Algebra

Let $x$ be the number of cupcakes and $y$ the number of cookies. Every item is one or the other, so the item count gives $x+y=50$. Prices don't belong in this equation.

Each cupcake brings in $2$ dollars, so $x$ cupcakes bring in $2x$ dollars. Each cookie brings in $1$ dollar, so $y$ cookies bring in $y$ dollars. The money total gives $2x+y=80$.

Type both equations into Desmos and click the intersection, where the lines cross. Desmos shows $(30,20)$; that point makes both totals true. The first coordinate is $x$, so Leah sold $30$ cupcakes, not $20$ cupcakes: $20$ is the cookie count. Choice C.

No Desmos needed. Replacing a cookie with a cupcake changes the money by exactly one dollar. If all $50$ items were $1 cookies, Leah would collect $50.

Replacing one cookie with one cupcake keeps the item count at $50$. Because cupcakes cost $2$ and cookies cost $1$, each replacement adds $1 to the money collected.

The actual total is $80$, which is $30 above the all-cookie amount: $80-50=30$. Each cupcake accounts for $1$ of that extra money, so Leah sold $30$ cupcakes. Choice C.