Question

Manny's Bakery recently spent a total of $600 on new equipment, and their average hourly operating costs are $5. Their average hourly receipts are $35. The bakery will soon make back the amount it invested in equipment. What would the total expenses and receipts both equal?Write a system of equations, graph them, and type the solution.

Answer 1

We are given taht a bakery has expenses that equal a fixed cost of $600 plus $5 for every hour of operating cost, this means that the expenses "E" are given by:

`E=600+5h`

Where:

`\begin{gathered} E=\text{ expenses} \\ h=\text{ operating hours} \end{gathered}`

We are also given that the receipts are $35 per hour, therefore, the receipts are given by:

`R=35h`

We get the system of equations:

`\begin{gathered} E=600+5h,(1) \\ R=35h,(2) \end{gathered}`

Now, we want to determine where both equations will have the same value. To do that we graph both equations and determine their point of minterception, as follows:

By graphing both equations we have obtained that the Expenses "E" and the Receipt "R" will intercept at the point

`(20,700)`

Where 20 represents the number of hours and 700 the total expenses and receipts.

Therefore, they both have the same value of $700.