Questions: Suppose you get a 80 music gift card. Each 1.29 song has an additional sales tax charge of 6% in your state. How many songs can you buy with the gift card? You can buy Jsong(s) with the gift card. (Type a whole number.)

Solution Steps

To determine how many songs you can buy with the gift card, you need to calculate the total cost of one song including the sales tax. Then, divide the total value of the gift card by the cost per song to find the number of songs you can purchase.

1. Calculate the total cost of one song including the sales tax.
2. Divide the total value of the gift card by the cost per song.
3. Use integer division to get the whole number of songs you can buy.

The cost of one song before tax is given as \( \$1.29 \). The sales tax rate is \( 6\% \), which can be expressed as \( 0.06 \). Therefore, the total cost of one song including sales tax is calculated as follows:

\[ \text{Total Song Cost} = \text{Song Price} \times (1 + \text{Sales Tax Rate}) = 1.29 \times (1 + 0.06) = 1.29 \times 1.06 = 1.3674 \]

The total value of the gift card is \( \$80 \). To find the number of songs that can be purchased, we divide the total value of the gift card by the total cost of one song:

\[ \text{Number of Songs} = \frac{\text{Gift Card Value}}{\text{Total Song Cost}} = \frac{80}{1.3674} \approx 58.5 \]

Since we can only purchase a whole number of songs, we take the integer part of this value:

\[ \text{Number of Songs} = 58 \]

Final Answer