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 [tex]=\dfrac{320-140}{4-1}=\dfrac{180}{3}=60[/tex]
Equation:
[tex]y-140=60(x-1)\\ \\y=60x-60+140\\ \\y=60x+80[/tex]
Quality Plumbing Company:
Slope [tex]=\dfrac{200-150}{1-0}=\dfrac{50}{1}=50[/tex]
Equation:
[tex]y-150=50(x-0)\\ \\y=50x+150[/tex]
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
[tex]60x+80=50x+150\\ \\60x-50x=150-80\\ \\10x=70\\ \\x=7[/tex]
Yes, they can charge the same amount of [tex]\$(50\cdot 7+150)=\$500[/tex] for 7 hours of work.
The cost of A plus plumbing cost for each hour of work is $140 and the one time fee is $80. The cost of quality plumbing cost for each hour of work is $200 and the one time fee is $150.
Given :
Two plumbing companies charge money for each hour of work, plus a one-time fee.
According to the graph given, there are two points on the line, that is (1,200) and (2,250).
So, the equation of the line that represents quality plumbing charges is given by:
[tex]\dfrac{y-200}{x-1}=\dfrac{250-200}{2-1}[/tex]
Simplify the above equation by cross multiplying.
y - 200 = 50(x - 1)
y - 200 = 50x - 50
y = 50x + 150 --- (1)
The equation of the line that represents A plus plumbing charges is given by:
[tex]\dfrac{y-140}{x-1}=\dfrac{320-140}{4-1}[/tex]
Simplify the above equation by cross multiplying.
3(y - 140) = 180(x - 1)
3y - 420 = 180x - 180
3y = 180x + 240
y = 60x + 80 --- (2)
A) The cost of A plus plumbing cost for each hour of work is given by:
y = 60(1) + 80
y = $140
So, the cost of A plus plumbing cost for each hour of work is $140.
The one time fee is determined by substituting (x = 0) in equation (2).
y = 60(0) + 80
y = $80
B) The cost of quality plumbing cost for each hour of work is given by:
y = 50(1) + 150
y = $200
The one time fee is determined by substituting (x = 0) in equation (1).
y = 50(0) + 150
y = $150
C) Given that cost of both the plumbing company are the same then the value of 'x' is given by:
50x + 150 = 60x + 80
70 = 10x
x = 7 hours
Yes, A plus plumbing and quality plumbing charge the same amount at the same amount of time of 7 hours.
For more information, refer to the link given below:
https://brainly.com/question/2263981
