Question

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

Trevor's Bakery recently spent a total of $98 on new equipment, and their average hourly operating costs are $8. Their average hourly receipts are $22. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal? How many hours will that take?

Answer 1

To determine the total expenses and receipts for Trevor's Bakery to break even, the equations are expenses E = 98 + 8x and receipts R = 22x. Solving the equation 22x = 98 + 8x for x, we find that it takes 7 hours for the bakery to make back its investment, where both total expenses and receipts equal $154.

Step-by-step explanation:

To solve the problem presented, we will first establish two equations to represent the total expenses and receipts for Trevor's Bakery as a function of the number of hours the bakery operates. Let 'x' represent the number of hours the bakery operates.

Equation for Total Expenses:

The total expenses (E) consist of a one-time investment of $98 for new equipment and the hourly operating costs of $8. Hence, the equation for total expenses is:

E = 98 + 8x

Equation for Total Receipts:

The total receipts (R) are given by the hourly receipts of $22 times the number of hours the bakery operates:

R = 22x

To find when the bakery will make back its investment, we set the total receipts equal to the total expenses:

22x = 98 + 8x

Subtract 8x from both sides of the equation to solve for x:

22x - 8x = 98

14x = 98

Divide both sides by 14 to find x:

x = 7

It will take 7 hours for the total expenses and receipts to be equal. At that point, they both will equal:

Total Expenses = Total Receipts = 22 * 7 = $154