Question

A group is selling chocolate-covered pretzels for 6 dollars per container and kettle corn for 8 dollars per container. They want to sell at least $2,800 in items. Part A Let c be the number of chocolate-covered pretzel containers sold and let k the number of kettle corn containers sold. Write three inequalities to represent the situation and the constraints of the variables. Part B Does selling 150 containers of chocolate-covered pretzels and 250 containers of kettle corn reach their goal? Explain your reasoning. Part C Explain what happens to the number of items they will need to sell if the price increases by 2 dollars for each item.

Answer 1

A) 6c + 8k ≥ 2800

6c ≥ 2800

8k ≥ 2800

B) Yes.

C) They will need to sell less items.

Explanation:

Given information

• Pretzels = $6 per container.
• Kettle Corn = $8 per container.

Definition of variables

• Let c be the number of chocolate-covered pretzel containers sold.
• Let k be the number of kettle corn containers sold.

Part A

If the group wants to sell at least $2,800 worth of items, the three inequalities to represent this will be:

Inequality 1

A combination of both items:

• 6c + 8k ≥ 2800

Inequality 2

The sale of pretzels only:

• 6c ≥ 2800

Inequality 3

The sale of kettle corn only:

• 8k ≥ 2800

Part B

Given:

• Selling 150 containers of pretzels ⇒ Let c = 150.
• Selling 250 containers of kettle corn ⇒ Let k = 250.

Substitute these values into the first inequality found in part A:

⇒ 6(150) + 8(250) ≥ 2800

⇒ 900 + 2000 ≥ 2800

⇒ 2900 ≥ 2800

As $2,900 is greater than $2,800, the group reached (and exceeded) their goal.

Part C

If the price increases by $2 for each item, they will need to sell less items to reach their goal.