QUESTION 14
Solve.
A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A
charges for the truck and per hour for the movers. Company B charges for the truck and per hour for the movers.
Create a cost equation for each company where y is the total cost and is the number of hours of labor. Write a system of equations.

Ask by Bradley Hammond. in the United States

Jan 19,2025

Question

QUESTION 14
Solve.
A couple have bought a new house and are comparing quotes from two moving companies for moving their furniture. Company A
charges for the truck and per hour for the movers. Company B charges for the truck and per hour for the movers.
Create a cost equation for each company where y is the total cost and is the number of hours of labor. Write a system of equations.

Ask by Bradley Hammond. in the United States

Jan 19,2025

UpStudy AI · Accepted Answer

To create cost equations for both companies, let's define the variables:

- $$ y $$: Total cost in dollars.
- $$ x $$: Number of hours of labor.

**Company A:**
- **Truck Charge:** \$110 (fixed cost)
- **Hourly Rate:** \$55 per hour

The total cost for Company A can be expressed as:
$$
y = 110 + 55x
$$

**Company B:**
- **Truck Charge:** \$90 (fixed cost)
- **Hourly Rate:** \$65 per hour

The total cost for Company B can be expressed as:
$$
y = 90 + 65x
$$

**System of Equations:**
$$
\begin{cases}
y = 110 + 55x \quad &\text{(Company A)} \
y = 90 + 65x \quad &\text{(Company B)}
\end{cases}
$$

This system represents the total costs for both companies based on the number of hours of labor ($$ x $$).
**Cost Equations:** - **Company A:** $$ y = 110 + 55x $$ - **Company B:** $$ y = 90 + 65x $$ **System of Equations:** $$ \begin{cases} y = 110 + 55x \ y = 90 + 65x \end{cases} $$

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