Question

evaluating and solving an equation application
identify the information given to you in the application problem below. use that information to answer the questions that follow.
round your answers to two decimal places as needed.
finn is a door to door vacuum salesman. his weekly salary $s(v)$ is given by the linear function $s(v)=340 + 80v$, where $v$ is the number of vacuums sold.
identify the slope, and complete the following sentence to explain the meaning of the slope.
finn earns $
per vacuum sold.
find the vertical intercept. complete the following sentence to explain the meaning of the vertical intercept.
if finn sells
vacuums, he will still earns a base salary of $
evaluate $s(40)$. complete the following sentence to explain the meaning of the ordered pair
if finn sells
vacuums, he will be paid $
find the value of $v$ where $s(v)=5060$.complete the following sentence to explain the meaning of the ordered pair.
for finn to earn $
, he needs to sell
vacuums.
question help: video message instructor

Explanation:

Step1: Identify slope of linear function

The linear - function is in the form $S(v)=340 + 80v$, which is in the slope - intercept form $y = mx + b$ where $m$ is the slope. Here, the slope $m = 80$. This means Finn earns $80$ per vacuum sold.

Step2: Find the vertical intercept

The vertical intercept of the linear function $S(v)=340 + 80v$ occurs when $v = 0$. Substituting $v = 0$ into the function, we get $S(0)=340+80\times0=340$. So if Finn sells $0$ vacuums, he will still earn a base salary of $340$.

Step3: Evaluate $S(40)$

Substitute $v = 40$ into the function $S(v)=340 + 80v$. Then $S(40)=340+80\times40=340 + 3200=3540$. So if Finn sells $40$ vacuums, he will be paid $3540$.

Step4: Solve for $v$ when $S(v)=5060$

Set $S(v)=5060$ in the equation $S(v)=340 + 80v$. So $5060=340 + 80v$. First, subtract $340$ from both sides: $5060−340=80v$, which gives $4720 = 80v$. Then divide both sides by $80$: $v=\frac{4720}{80}=59$. So for Finn to earn $5060$, he needs to sell $59$ vacuums.

Answer:

Finn earns $80$ per vacuum sold.
If Finn sells $0$ vacuums, he will still earn a base salary of $340$.
If Finn sells $40$ vacuums, he will be paid $3540$.
For Finn to earn $5060$, he needs to sell $59$ vacuums.