When Millie called​ Pete's Plumbing, Pete worked 3 hours and charged Millie $155. When Rosalee called​ Pete, he worked 66 hours and charged 230. If​ Pete's charge is a linear function of the number of hours​ worked, find the formula for​ Pet?

1 Answer
Dec 8, 2017

f(x) = hx+b
where h is Pete's charge per hour and b is his fixed charge irrespective of the hours and x is time in hours.
f(x) = 1.19x + 151.43

Explanation:

155 = 3x +b
230 = 66x+b
x = (155-b)/3
x = (230-b)/66
(155-b)/3 = (230-b)/66
multiply both side by 66
3410-22b = 230-b
-21b = -3180
b = 151.43 (rounded to two decimals)
x = (155-151.43)/3 = 3.57/3 = 1.19
Now write the linear function
f(x) = 1.19x + 151.43