Question 1

Question

A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7 per shirt to earn the remaining money.
Part A
Complete the inequality to represent the minimum number of shirts, n, the band must sell to earn the remaining money.
Drag tiles to the empty boxes to complete the inequality correctly.
Put responses in the correct input to answer the question.
7[blankN [blank] 700 [blank] 1,150
≤ − ÷ < > ≥ + ⋅
Question 2
Part B
What is the minimum number of shirts the band must sell to earn the remaining money?
Enter your answer in the box.
shirts

Answer 1

To solve this problem, we will complete the inequality in Part A and then calculate the minimum number of shirts in Part B.

Part A: Completing the Inequality

The band needs at least $1,150 to cover expenses, and they have already saved $700. This means they need to earn at least:

\[ 1,150 - 700 = 450 \text{ dollars} \]

They earn a profit of $7 per shirt, so the amount they earn from selling \( n \) shirts is \( 7n \).

The inequality representing the minimum number of shirts, \( n \), that they must sell to earn at least $450 is:

\[ 7n \geq 450 \]

Now, we place the correct tiles in the blanks:

7 [n] [≥] 700 [+] 1,150

Part B: Calculating the Minimum Number of Shirts

To find the minimum number of shirts, we will solve the inequality:

\[ 7n \geq 450 \]

Dividing both sides by 7:

\[ n \geq \frac{450}{7} \]

Calculating that:

\[ n \geq 64.2857 \]

Since the band cannot sell a fraction of a shirt, we round up to the next whole number:

\[ n \geq 65 \]

Thus, the minimum number of shirts the band must sell is 65.

Final Answers:

• Part A: 7 [n] [≥] 700 [+] 1,150
• Part B: 65 shirts