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Question 1 (1 point)

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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)

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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)

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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)

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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)

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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

1 answer

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