Question

Courtney purchases a total of 87 books for a total of $200. Some books sell for $4 and others are on sale for $2. How many $4 books does she buy?

Answer 1

Let 'x' be the number of books that cost $4 and let 'y' be the number of books that cost $2. Since Courtney purchased 87 books, then we have the following equation:

`x+y=87`

also, she spent a total of $200, then, we have the next equation:

`4x+2y=200`

we want to know how many $4 books Courtney bought. Then, in the first equation, we can solve for y to get the following:

`y=87-x`

if we substitute this equation on the second equation, we get:

`\begin{gathered} 4x+2(87-x)=200 \\ \Rightarrow4x+174-2x=200 \\ \Rightarrow4x-2x=200-174 \\ \Rightarrow2x=26 \\ \Rightarrow x=(26)/(2)=13 \\ x=13 \end{gathered}`

therefore, Courtney purchased 13 books that cost $4