Question

end-of-unit assessment (continued)name7. two plumbing companies charge for each hour of work, plus a one-time fee.quality plumbing charges according to this graph.a-plus plumbing charges according to this table.| time (hr) | cost (dollars) || ---- | ---- || 1 | 140 || 4 | 320 || 6 | 440 |a how much does quality plumbing charge for each hour?what is the one-time fee?show or explain your thinking.b how much does a-plus plumbing charge for each hour?what is the one-time fee?show or explain your thinking.c is the cost of using quality plumbing or a-plus plumbing ever the same for the same amount of time? circle one.yes noshow or explain your thinking.

Explanation:

Step1: Find Quality Plumbing hourly rate

From the graph, at $t=0$, cost = $150 (one-time fee). At $t=3$, cost = $300. Hourly rate: $\frac{300-150}{3} = 50$

Step2: Confirm Quality one-time fee

At $t=0$, cost = $150, so one-time fee = $150

Step3: Find A-Plus Plumbing hourly rate

From the table: $\frac{320-140}{4-1} = \frac{180}{3} = 60$

Step4: Confirm A-Plus one-time fee

Use $t=1$, cost = $140$. Fee = $140 - (1\times60) = 80$

Step5: Set costs equal, solve for $t$

Let $C_Q = 50t + 150$, $C_A = 60t + 80$. Set equal:
$50t + 150 = 60t + 80$
$150-80 = 60t-50t$
$70 = 10t$
$t=7$
Since $t=7$ is a valid positive time, costs are equal.

Answer:

a. Hourly charge: $\$50$; One-time fee: $\$150$
b. Hourly charge: $\$60$; One-time fee: $\$80$
c. Yes; The costs are equal at 7 hours of work.