Let's break down the problem step by step.
Total expenses needed: $1,150
Amount already saved: $700
Profit per shirt: $7
Remaining amount needed:
To find the remaining amount the band needs to earn, we subtract the amount they've already saved from the total expenses:
\[
\text{Remaining Amount} = 1,150 - 700 = 450
\]
Setting up the inequality:
Let \( n \) be the number of shirts the band needs to sell. The profit made from selling \( n \) shirts can be expressed as \( 7n \). To cover the remaining expenses, we set up the inequality:
\[
7n \geq 450
\]
Therefore, the complete inequality would be: \[ 7n \geq 450 \]
In your given format: \[ 7[≥]n[≥]700[+ ]1,150 \]
Now, moving to Part B where we need to find the minimum number of shirts to sell:
To find \( n \), we can solve the inequality: \[ 7n \geq 450 \]
Dividing both sides by 7: \[ n \geq \frac{450}{7} \] \[ n \geq 64.2857... \]
Since the band cannot sell a fraction of a shirt, they must sell at least: \[ n = 65 \text{ shirts} \]
Thus, the answers to your questions are:
- Part A: Complete inequality: \( 7n ≥ 450 \)
- Part B: Minimum number of shirts: 65 shirts.