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Question 2477: The charge for Yellow's Yard Service is a linear function of the number of hours the yard work
takes. Len was charged $44 for three hours of yard work, while his neighbor Mavis was charged
$60 for five hours of work. Write the cost C of having Yellow's work on a lawn as a function
of the number of hours n it takes them to finish the work
Thanks in advance for your help!!
Answer by AnlytcPhil(1806)   (Show Source):
You can put this solution on YOUR website! >>...The charge for Yellow's Yard Service is a linear function of the number of hours the yard work takes. Len was charged $44 for three hours of yard work, while his neighbor Mavis was charged $60 for five hours of work. Write the cost C of having Yellow's work on a lawn as a function of the number of hours n it takes them to finish the work Thanks in advance for your help!!...<<
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>>...Len was charged $44 for three hours of yard work,...<<
>>...the cost C...<<
>>...number of hours n...<<
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Translation: when n = 3, C = 44
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>>...Mavis was charged $60 for five hours of work...<<
>>...the cost C...<<
>>...number of hours n...<<
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translation: when n = 5, C = 60
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We turn this into the problem:
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Write the equation of the line which passes through the two points (3, 44) and (5, 60)
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Use slope formula:
m = (y2 - y1)/(x2 - x1)
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m = (60 - 44)/(5 - 3) = 16/2 = 8
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Use point-slope fomula:
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y = y1 = m(x - x1)
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y - 44 = 8(x - 3)
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y - 44 = 8x - 24
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y = 8x + 20
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Now we change y to C and x to n
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C = 8n + 20
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Check: Substitute n=3 and get C = 8(3) + 20 = 24+20 = 44
Substitute n=5 and get C = 8(5) + 20 = 40+20 = 60
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Edwin
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