A food truck selling gourmet grilled cheese sandwiches has a daily fixed operating cost of… — ACT

A food truck selling gourmet grilled cheese sandwiches has a daily fixed operating cost of $120$ . Each sandwich costs $2.50$ to make and is sold for $6.50$ . What is the minimum number of sandwiches the food truck must sell in one day to make a net profit of at least $180$ ?

Answer: 75 sandwiches

Answer

The food truck must sell a minimum of 75 sandwiches to make a net profit of at least $180.

Representing the number of sandwiches sold as

x

, the total revenue is

6.50x

and the total cost is

120 + 2.50x

. The net profit is the difference between revenue and cost:

6.50x - (120 + 2.50x)

, which simplifies to

4x - 120

. Setting up the inequality for a profit of at least

180

gives

4x - 120 \geq 180

. Solving for

x

gives

4x \geq 300

, which simplifies to

x \geq 75

. Therefore, the minimum number of sandwiches that must be sold is

75

Step-by-Step Solution

Define the variable and write expressions for revenue and cost.

Let

x

represent the number of sandwiches sold. Total Revenue =

6.50x

and Total Cost =

120 + 2.50x

Defining the variable and translating the verbal descriptions of revenue and cost into algebraic expressions is necessary to model the profit.

Formulate the net profit expression.

Net Profit = Total Revenue - Total Cost =

6.50x - (120 + 2.50x) = 4x - 120

Net profit is calculated by subtracting all fixed and variable costs from the total revenue.

Set up and solve the linear inequality.

4x - 120 \geq 180 \Rightarrow 4x \geq 300 \Rightarrow x \geq 75

To find the minimum number of sandwiches needed to reach a target profit of at least

180

, we solve the inequality

4x - 120 \geq 180

for

x

Key Concept

Translating a real-world scenario into a linear inequality and solving for the unknown variable.

Question

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