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
Thomas Kanat
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#

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