a salesperson earns a commission based on the number and type of vehicle sold. a person selling 6 cars and 3…
a salesperson earns a commission based on the number and type of vehicle sold. a person selling 6 cars and 3 trucks earns $4,800. a person selling 8 cars and 1 truck earns $4,600. how much does a salesperson earn for selling 2 cars and 3 trucks?\n$2,500\n$2,700\n$2,800\n$3,000
Answer
Explanation:
Step1: Set up equations
Let $x$ be the commission for selling a car and $y$ be the commission for selling a truck. We get the system of equations: $$\begin{cases}6x + 3y=4800\8x + y=4600\end{cases}$$
Step2: Solve for $y$ in the second - equation
From $8x + y=4600$, we have $y = 4600 - 8x$.
Step3: Substitute $y$ into the first equation
Substitute $y = 4600 - 8x$ into $6x+3y = 4800$: $6x+3(4600 - 8x)=4800$. Expand: $6x + 13800-24x=4800$. Combine like - terms: $- 18x=4800 - 13800=-9000$. Solve for $x$: $x = 500$.
Step4: Solve for $y$
Substitute $x = 500$ into $y = 4600 - 8x$, we get $y=4600-8\times500=4600 - 4000 = 600$.
Step5: Calculate the commission for 2 cars and 3 trucks
The commission for selling 2 cars and 3 trucks is $2x+3y$. Substitute $x = 500$ and $y = 600$: $2\times500+3\times600=1000 + 1800=2800$.
Answer:
$2800$ (corresponding to the third option)