Answer :
To solve the problem of determining a formula that models the cost of buying video games during a sale, follow these steps:
1. Understand the Pricing Model:
- The cost of the first video game is [tex]$40.
- Each additional video game costs $[/tex]25.
2. Define the Variable:
- Let [tex]\( n \)[/tex] be the total number of video games you buy.
3. Develop the Formula:
- If you buy just one game ([tex]\( n = 1 \)[/tex]), the cost is [tex]$40.
- If you buy more than one game, you pay $[/tex]40 for the first game and [tex]$25 for each of the remaining \( n-1 \) games.
4. Formulate the Expression:
- The cost for the first game is $[/tex]40.
- The cost for the additional [tex]\( n-1 \)[/tex] games is [tex]\((n-1) \times 25\)[/tex].
- Add these two parts together to get the total cost:
[tex]\[ a_n = 40 + (n-1) \times 25 \][/tex]
This formula will give you the total cost of buying [tex]\( n \)[/tex] video games during the sale.
1. Understand the Pricing Model:
- The cost of the first video game is [tex]$40.
- Each additional video game costs $[/tex]25.
2. Define the Variable:
- Let [tex]\( n \)[/tex] be the total number of video games you buy.
3. Develop the Formula:
- If you buy just one game ([tex]\( n = 1 \)[/tex]), the cost is [tex]$40.
- If you buy more than one game, you pay $[/tex]40 for the first game and [tex]$25 for each of the remaining \( n-1 \) games.
4. Formulate the Expression:
- The cost for the first game is $[/tex]40.
- The cost for the additional [tex]\( n-1 \)[/tex] games is [tex]\((n-1) \times 25\)[/tex].
- Add these two parts together to get the total cost:
[tex]\[ a_n = 40 + (n-1) \times 25 \][/tex]
This formula will give you the total cost of buying [tex]\( n \)[/tex] video games during the sale.
