Question
25. A music streaming service is having a sale. Regularly, songs cost $1.29 each and videos are $1.99, but today there is a 20% discount on both. If Raj wants to buys songs and v videos, which expression represents the amount of money he can save by making his purchase today rather than tomorrow?
Answers
GPT-4o mini
To determine the savings Raj can achieve by making his purchase today with the 20% discount, we first need to calculate the regular prices and the discounted prices for the songs and videos:
1. **Regular Prices:**
- The regular price of a song: $1.29
- The regular price of a video: $1.99
2. **Discounted Prices:**
- The discount on a song (20% of $1.29) is:
\[
0.20 \times 1.29 = 0.258
\]
Thus, the discounted price for a song is:
\[
1.29 - 0.258 = 1.29 - 0.258 = 1.032
\]
- The discount on a video (20% of $1.99) is:
\[
0.20 \times 1.99 = 0.398
\]
Thus, the discounted price for a video is:
\[
1.99 - 0.398 = 1.99 - 0.398 = 1.592
\]
3. **Total Cost Today with Discounts:**
- Total cost of Raj's purchase today, if he buys \( s \) songs and \( v \) videos, would be:
\[
\text{Total Today} = s \times 1.032 + v \times 1.592
\]
4. **Total Cost Tomorrow (No Discounts):**
- Total cost of Raj's purchase tomorrow, if he buys \( s \) songs and \( v \) videos, would be:
\[
\text{Total Tomorrow} = s \times 1.29 + v \times 1.99
\]
5. **Amount Saved by Buying Today:**
- The amount saved by purchasing today rather than tomorrow is the difference between the total cost tomorrow and the total cost today:
\[
\text{Savings} = \text{Total Tomorrow} - \text{Total Today}
\]
- Substituting the expressions for total costs:
\[
\text{Savings} = (s \times 1.29 + v \times 1.99) - (s \times 1.032 + v \times 1.592)
\]
6. **Final Savings Expression:**
\[
\text{Savings} = s \times 1.29 + v \times 1.99 - s \times 1.032 - v \times 1.592
\]
Combining like terms gives us:
\[
\text{Savings} = s \times (1.29 - 1.032) + v \times (1.99 - 1.592)
\]
Calculating the individual savings:
\[
1.29 - 1.032 = 0.258 \quad \text{and} \quad 1.99 - 1.592 = 0.398
\]
Thus, the expression for the amount of money Raj can save is:
\[
\text{Savings} = s \times 0.258 + v \times 0.398
\]
1. **Regular Prices:**
- The regular price of a song: $1.29
- The regular price of a video: $1.99
2. **Discounted Prices:**
- The discount on a song (20% of $1.29) is:
\[
0.20 \times 1.29 = 0.258
\]
Thus, the discounted price for a song is:
\[
1.29 - 0.258 = 1.29 - 0.258 = 1.032
\]
- The discount on a video (20% of $1.99) is:
\[
0.20 \times 1.99 = 0.398
\]
Thus, the discounted price for a video is:
\[
1.99 - 0.398 = 1.99 - 0.398 = 1.592
\]
3. **Total Cost Today with Discounts:**
- Total cost of Raj's purchase today, if he buys \( s \) songs and \( v \) videos, would be:
\[
\text{Total Today} = s \times 1.032 + v \times 1.592
\]
4. **Total Cost Tomorrow (No Discounts):**
- Total cost of Raj's purchase tomorrow, if he buys \( s \) songs and \( v \) videos, would be:
\[
\text{Total Tomorrow} = s \times 1.29 + v \times 1.99
\]
5. **Amount Saved by Buying Today:**
- The amount saved by purchasing today rather than tomorrow is the difference between the total cost tomorrow and the total cost today:
\[
\text{Savings} = \text{Total Tomorrow} - \text{Total Today}
\]
- Substituting the expressions for total costs:
\[
\text{Savings} = (s \times 1.29 + v \times 1.99) - (s \times 1.032 + v \times 1.592)
\]
6. **Final Savings Expression:**
\[
\text{Savings} = s \times 1.29 + v \times 1.99 - s \times 1.032 - v \times 1.592
\]
Combining like terms gives us:
\[
\text{Savings} = s \times (1.29 - 1.032) + v \times (1.99 - 1.592)
\]
Calculating the individual savings:
\[
1.29 - 1.032 = 0.258 \quad \text{and} \quad 1.99 - 1.592 = 0.398
\]
Thus, the expression for the amount of money Raj can save is:
\[
\text{Savings} = s \times 0.258 + v \times 0.398
\]