Question

end-of-unit assessment7. 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:

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Part a

Step1: Identify one-time fee

The y-intercept (time=0) is the one-time fee: $\$150$

Step2: Calculate hourly rate

Use 3 hours of work: Cost at 3hr is $\$300$. Subtract one-time fee: $\$300 - \$150 = \$150$. Divide by hours: $\frac{150}{3} = 50$
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Part b

Step1: Calculate hourly rate

Use 1hr and 4hr costs: $\$320 - \$140 = \$180$ over 3 hours. Hourly rate: $\frac{180}{3} = 60$

Step2: Find one-time fee

Subtract hourly cost from 1hr total: $\$140 - (1 \times 60) = 80$
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Part c

Step1: Write cost equations

Quality Plumbing: $C_Q = 50t + 150$
A-Plus Plumbing: $C_A = 60t + 80$

Step2: Set equations equal

$50t + 150 = 60t + 80$

Step3: Solve for t

$150 - 80 = 60t - 50t$
$70 = 10t$
$t = 7$
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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.