Two plumbers charge an initial fee and an hourly rate.
The equation y = 100 + 30x models plumber A's fee, where y is the total charge, in dollars, and x is the number of
hours worked
The table shown represents plumber B's total charge for different numbers of hours.
Plumber B
Hours Total Charges ($)
1
105
2.
160
3
215
2.
Part A: Which plumber charges more money per hour? Explain how you know.
Part B: Which plumber charges a higher initial fee? Explain how you know.
Part C: Which plumber charges less money for working 5 hours? Show your work to justify your answer.
Answers
Answer:
A) Plumber B charges 55 dollars per hour (105=50+55(1)) because for 1 hour the total is 105, meaning that 105 is y and 1 is x. 50+55=105
B) Plumber A charges more because he charges 100 dollars vs Plumber B's 50 dollars.
C) Plumber A: 250=100+30(5) Plumber B: 325=50+55(5)
Plumber A charges less money for working 5 hours.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that,
Two plumbers charge an initial fee and an hourly rate.
The equation y=100+30x -----(I) models plumber A's fee, where y is the total charge, in dollars, and x is the number of hours worked.
Part A:
From the table, we have (1, 105) and (2, 160)
Now, m=(160-105)/(2-1)
= 55
Substitute m=55 and (x, y)=(1, 105) in y=mx+c, we get
105=55(1)+c
c=60
Substitute m=55 and c=60 in y=mx+c, we get
y=55x+60 -----(II)
By comparing (I) and (II), we can conclude that plumber B charges more hourly fee.
Part B: By comparing (I) and (II), we can conclude that plumber A charges more initial fee.
Part C: Substitute x=5 in y=100+30x, we get
y=$250
Substitute x=5 in y=55(5)+60, we get
y=$335
Plumber A charges less money for working 5 hours.
Therefore, plumber A charges more initial fee.
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