Question

You and a friend are starting a computer repair business. You estimate that yourexpenses are $500 per week.Select a reasonable average number of dollars you would expect to spend(expense) on replacement parts for each computer you repair. Then decide on anaverage fee that you will charge for each computer you repair (income). Let xrepresent the number of computers you repair each week.Write a linear equation that describes your total weekly expenses.Write a linear equation that describes your total weekly income.

Answer 1

Let:

E = Expenses

I = Income

x = number of computers you repair each week

a = average fee that you will charge for each computer you repair

b = cost of replacement parts for each computer

$\begin{gathered} E=bx \\ 500=bx \end{gathered}$

Let's assume you repair 30 computers per week:

$\begin{gathered} 500=bx \\ x=30 \\ 500=b(30) \\ b=\frac{500}{30} \\ b=16.67 \end{gathered}$

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Now, since the incomes must be greater than the expenses:

$\begin{gathered} I=ax \\ I>E \\ so\colon \\ ax>500 \\ \text{let:} \\ x=30 \\ a>\frac{500}{30} \\ a>16.67 \\ a=17 \end{gathered}$