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:
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Regular Prices:
- The regular price of a song: $1.29
- The regular price of a video: $1.99
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Discounted Prices:
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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: \[ 1.29 - 0.258 = 1.29 - 0.258 = 1.032 \]
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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: \[ 1.99 - 0.398 = 1.99 - 0.398 = 1.592 \]
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Total Cost Today with Discounts:
- Total cost of Raj's purchase today, if he buys \( s \) songs and \( v \) videos, would be: \[ \text{Total Today} = s \times 1.032 + v \times 1.592 \]
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Total Cost Tomorrow (No Discounts):
- Total cost of Raj's purchase tomorrow, if he buys \( s \) songs and \( v \) videos, would be: \[ \text{Total Tomorrow} = s \times 1.29 + v \times 1.99 \]
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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: \[ \text{Savings} = (s \times 1.29 + v \times 1.99) - (s \times 1.032 + v \times 1.592) \]
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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: \[ \text{Savings} = s \times 0.258 + v \times 0.398 \]