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Carol downloads x songs at 99 cents each...

Carol downloads x songs at 99 cents each , and y e-books at $2.99 each. Altogether she buys 11 items , where an item is a song or an e-book . The total amount of money she spends on this transaction is $22.89 . Solving which of the following equations correctly yields y , the number of e-books ?

A

0.99(11-y)+2.99y=22.89

B

0.99(11+y) + 2.99y = 22.89

C

2.99(11-y)+0.99 y = 22.89

D

2.99(11+y) + 0.99 y =22.89

Text Solution

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To solve the problem, we need to set up equations based on the information given about Carol's purchases. ### Step-by-Step Solution: 1. **Define the Variables**: - Let \( x \) be the number of songs Carol downloads. - Let \( y \) be the number of e-books Carol buys. 2. **Set Up the Equations**: - According to the problem, Carol buys a total of 11 items (songs and e-books). This can be expressed as: \[ x + y = 11 \] - The cost of each song is $0.99, and the cost of each e-book is $2.99. The total amount spent is $22.89. This can be expressed as: \[ 0.99x + 2.99y = 22.89 \] 3. **Express \( x \) in terms of \( y \)**: - From the first equation \( x + y = 11 \), we can express \( x \) as: \[ x = 11 - y \] 4. **Substitute \( x \) into the second equation**: - Now substitute \( x \) in the second equation: \[ 0.99(11 - y) + 2.99y = 22.89 \] 5. **Distribute and Simplify**: - Distributing \( 0.99 \): \[ 10.89 - 0.99y + 2.99y = 22.89 \] - Combine like terms: \[ 10.89 + (2.99 - 0.99)y = 22.89 \] \[ 10.89 + 2.00y = 22.89 \] 6. **Isolate \( y \)**: - Subtract \( 10.89 \) from both sides: \[ 2.00y = 22.89 - 10.89 \] \[ 2.00y = 12.00 \] - Divide both sides by 2: \[ y = 6 \] ### Final Answer: The number of e-books \( y \) that Carol buys is \( 6 \).
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