Question
An entertainment firm offers several DJ choices and light shows that range in price based on the rental time period. The DJ's cost between $219
and $369
per night and the light shows cost between 159.00$
and $309
per night. If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay,
.
.
and $369
per night and the light shows cost between 159.00$
and $309
per night. If you are booking both a DJ and a light show, write a compound inequality that represents the possible total amount you would pay,
.
.
Answers
GPT-4o mini
To represent the total cost of booking both a DJ and a light show, we need to consider the minimum and maximum costs for each.
1. **DJ Costs:**
- Minimum cost of a DJ: $219
- Maximum cost of a DJ: $369
2. **Light Show Costs:**
- Minimum cost of a light show: $159
- Maximum cost of a light show: $309
Now, we can calculate the minimum and maximum total costs when booking both:
- **Minimum Total Cost**:
- Minimum DJ cost + Minimum light show cost = \( 219 + 159 = 378 \)
- **Maximum Total Cost**:
- Maximum DJ cost + Maximum light show cost = \( 369 + 309 = 678 \)
Therefore, the total cost when booking both a DJ and a light show can be represented by the compound inequality:
\[
378 \leq x \leq 678
\]
where \( x \) represents the total amount you would pay for both services.
1. **DJ Costs:**
- Minimum cost of a DJ: $219
- Maximum cost of a DJ: $369
2. **Light Show Costs:**
- Minimum cost of a light show: $159
- Maximum cost of a light show: $309
Now, we can calculate the minimum and maximum total costs when booking both:
- **Minimum Total Cost**:
- Minimum DJ cost + Minimum light show cost = \( 219 + 159 = 378 \)
- **Maximum Total Cost**:
- Maximum DJ cost + Maximum light show cost = \( 369 + 309 = 678 \)
Therefore, the total cost when booking both a DJ and a light show can be represented by the compound inequality:
\[
378 \leq x \leq 678
\]
where \( x \) represents the total amount you would pay for both services.