# 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. # 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.

Question
Systems of equations
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. ## Answers (1) 2021-02-13 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 {b+c=7,6b+9c=54}

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