At a book sale, novels sell for $6 each and nonfiction books sell for $10 each. If Mike purchased 10 books for a total cost of $88 at the book sale, how many novels did he purchase?

Summary Submit Skip Question

We can set up a equation for the total number of books and the cost of the books.

$$ \text{novel} + \text{non-fiction} = \text{total books} $$ $$ A + B = 10 $$ $$ \text{cost of novels}+\text{cost of non-fiction books} = \text{total cost} $$ $$ 6A+10B=88 $$

We are looking for the number of novels, so let's substitute or eliminate the non-fiction variables (\(B\) in this case). Multiplying the first equation by 10:

$$ A+B=10 $$ $$ 10A+10B=100 $$

Using elimination

$$ \begin{array}{c c c} &10A & 10B & 100 \\ -&6A & 10B & 88 \\ \hline & 4A & 0 & 12 \end{array} $$ $$4A=12 $$ $$A=\boxed{3} $$

We can test the answer choices. Here is the process for testing the correct answer choice, \(\boxed{3} \).

The cost of 3 novels is $18. Since there are 10 books in total, there must be 7 nonfiction books. 7 nonfiction books would cost $70. $18+$70=$88, which matches our situation.