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?

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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.