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?

1 answer

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: \[ \text{Savings} = s \times 0.258 + v \times 0.398 \]