You are provided with the variable expense equation for a coffee shop. Use this equation and their fixed expenses to determine the final total expenses equation.

Fixed expenses:

Rent: \$2,200
Insurance: \$300
Equipment lease: \$500

Variable expenses equation: $V(q)=1.75 q+250$, where $q$ is the quantity of items.

The final total expenses equation for the coffee shop is $E(q)=1.75 q+$ □ .

A800
B2,750
C3,250
D1,950

Question

01-11-2026
Mathematics

Answered

You are provided with the variable expense equation for a coffee shop. Use this equation and their fixed expenses to determine the final total expenses equation.

Fixed expenses:

Rent: \$2,200
Insurance: \$300
Equipment lease: \$500

Variable expenses equation: $V(q)=1.75 q+250$, where $q$ is the quantity of items.

The final total expenses equation for the coffee shop is $E(q)=1.75 q+$ □ .

A800
B2,750
C3,250
D1,950

Verified Answer :

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GinnyAnswer GinnyAnswer · Answer 1 · 2026-11-01T11:38:27-05:00

Identify the fixed expenses as $\$2,200 + \$300 + \$500 = \$3,000$.
Recognize the variable expenses equation as $V(q) = 1.75q + 250$.
Sum the fixed costs with the variable cost constant to get $E(q) = 1.75q + (250 + 3000) = 1.75q + 3250$.
Match the constant $3250$ to option c.
The final equation is $E(q) = 1.75q + \boxed{3250}$.

Explanation

Analysis of Expenses

To find the total expenses equation $E(q)$, we must aggregate both fixed and variable costs. The fixed expenses are given as rent ($\$2,200$), insurance ($\$300$), and equipment lease ($\$500$). The variable expenses are expressed by the function $V(q) = 1.75q + 250$, where $q$ represents the number of items sold. The total expense function is the sum of these, denoted as $E(q) = V(q) + \text{Fixed Expenses}$.

Calculating Total Fixed Expenses

First, we calculate the total sum of all fixed expenses ($F$):
\[F = 2200 + 300 + 500\]
Summing these values:
\[2200 + 300 = 2500\]
\[2500 + 500 = 3000\]
So, the total fixed expense is $\$3,000$.

Formulating the Total Expenses Equation

Now, we combine the total fixed expenses with the variable expenses equation to determine the complete equation $E(q)$. Given $V(q) = 1.75q + 250$:
\[E(q) = (1.75q + 250) + 3000\]
We group the constant terms together:
\[E(q) = 1.75q + (250 + 3000)\]
\[E(q) = 1.75q + 3250\]
The constant term in the total expenses equation is $3250$. Comparing this result with the provided options (a. 800, b. 2750, c. 3250, d. 1950), the correct choice is c.

Examples

Understanding how to combine fixed and variable costs is essential for any business owner, such as a coffee shop manager, to determine their break-even point and overall profitability. By correctly adding fixed costs like rent and insurance to the variable costs of ingredients per cup of coffee, a manager can create a clear financial model to price their products effectively and ensure the business remains sustainable. This mathematical approach helps in making informed decisions about daily operations and long-term financial planning.