Question

Two plumbing companies charge money for each hour of work, plus a one-time fee

Answer 1

Answer:

a. A Plus Plumbing company charges $60 per hour and $80 as one-time fee

b. Quality Plumbing company charges $50 per hour and $150 as one-time fee

c. Yes, they can charge the same amount of $500 for 7 hours of work.

Step-by-step explanation:

Write the linear functions representing both companies charges

A Plus Plumbing Company:

Slope $=\dfrac{320-140}{4-1}=\dfrac{180}{3}=60$

Equation:

$y-140=60(x-1)\\ \\y=60x-60+140\\ \\y=60x+80$

Quality Plumbing Company:

Slope $=\dfrac{200-150}{1-0}=\dfrac{50}{1}=50$

Equation:

$y-150=50(x-0)\\ \\y=50x+150$

a. A Plus Plumbing company charges $60 per hour and $80 as one-time fee

b. Quality Plumbing company charges $50 per hour and $150 as one-time fee

c. Suppose they charge the same amount of money, then

$60x+80=50x+150\\ \\60x-50x=150-80\\ \\10x=70\\ \\x=7$

Yes, they can charge the same amount of $\ (50\cdot 7+150)=\ 500$ for 7 hours of work.