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
asked 2021-02-12
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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