Question

Question 1 (1 point)

Listen
A manager is comparing the cost of buying baseball caps from two different companies. Company X charges a $50 fee plus $7 per cap. Company Y charges a $30 fee plus $9 per cap. Which inequality can be used to determine for what number of caps Company X is cheaper?

Question 1 options:








Question 2 (1 point)

Listen
Jamal has $15.00 to spend at the Owl's nest. He buys nachos for $7.50 and he wants to purchase some boxes of candy for $1.75 each. Which inequality can be used to determine the number of boxes of candy he can purchase?

Question 2 options:








Question 3 (1 point)

Listen
Greg is saving for a new cell phone that will cost him $550. He already has $300 saved. If he wants to buy the phone in 4 weeks, which inequality can be used to determine the amount of money he needs to save each week to have at least $550?

Question 3 options:








Question 4 (1 point)

Listen
A manager is comparing the cost of buying baseball caps from two different companies. Company X charges a $50 fee plus $7 per cap. Company Y charges a $30 fee plus $9 per cap. For what number of caps is Company X cheaper?

Question 4 options:

More than 10 caps


Exactly 10 caps


Less than 10 caps


Company X will always be more expensive

Question 5 (1 point)

Listen
Jamal has $15.00 to spend at the Owl's nest. He buys nachos for $7.50 and he wants to purchase some boxes of candy for $1.75 each. How many boxes of candy can Jamal purchase?

Question 5 options:

He can buy 4.3 boxes of candy


4 or more boxes of candy


4 or fewer boxes of candy


At least 4 boxes of candy

Answer 1

Let's break down each question step by step:

### Question 1:
To find the inequality for comparing the costs of Company X and Company Y:

**Company X:**
Cost = $50 + $7x (where x is the number of caps)

**Company Y:**
Cost = $30 + $9x

To find when Company X is cheaper than Company Y:
\[
50 + 7x < 30 + 9x
\]
Rearranging gives:
\[
50 - 30 < 9x - 7x
\]
\[
20 < 2x
\]
or
\[
10 < x
\]
So, the inequality is:
**x > 10**

### Question 2:
Jamal has $15.00. He spends $7.50 on nachos and wants to buy boxes of candy that cost $1.75 each.

Remaining money after buying nachos:
\[
15.00 - 7.50 = 7.50
\]
Let y be the number of boxes of candy.
The inequality is:
\[
1.75y \leq 7.50
\]

### Question 3:
Greg needs $550 for a new cell phone, he currently has $300, and he wants to buy it in 4 weeks:

Amount needed to save:
\[
550 - 300 = 250
\]
If x is the amount he needs to save each week:
\[
4x \geq 250
\]
So the inequality is:
**x ≥ 62.5**

### Question 4:
We found that Company X is cheaper when:
**x > 10 caps.**

### Question 5:
Using the remaining money after buying nachos:
He can spend $7.50 on candy, and each box of candy costs $1.75:

Calculating maximum boxes of candy:
\[
7.50 ÷ 1.75 ≈ 4.29
\]
Thus, he can buy:
**4 or fewer boxes of candy.**

### Summary of Answers:
1. For Company X to be cheaper: **x > 10**
2. Jamal's inequality for boxes of candy: **1.75y ≤ 7.50**
3. Greg's inequality for saving: **x ≥ 62.5**
4. For number of caps where Company X is cheaper: **More than 10 caps**
5. Number of boxes of candy Jamal can purchase: **4 or fewer boxes of candy**