# Manuel has $54 to buy CDs and books. Each CD costs$9, and each book costs $6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys. Phoebe 2021-02-12 Answered Manuel has$54 to buy CDs and books. Each CD costs $9, and each book costs$6. He wants to buy exactly 7 items to spend all of his money. Write a system of equations that could be solved to determine the number of CDs and the number of books Manuel buys.
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Let c be the number of CDs and b be the number of books that he buys.
Since he buys exactly 7 items, then $b+c=7$.
If each CD costs $9 dollars, then he will spend 9c dollars buying cc CDs. If each book costs$6, then he will spend 6b dollars buying bb books. The total amount he spends is then $6b+9c$. Since he has \$54 to spend, then $6b+9c=54$.
The system of equations is then $\left\{b+c=7,6b+9c=54\right\}$