SOLUTION: A carpenter charges $42 per hour for his time and $24 per hour for his apprentice's time. On a certain job the apprentice does some preparatory work alone and then the carpenter fi

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Question 805527: A carpenter charges $42 per hour for his time and $24 per hour for his apprentice's time. On a certain job the apprentice does some preparatory work alone and then the carpenter finishes the job alone. If the job took a total of 10 hours and the total bill was $325.5, how long did the carpenter work ?
Select the correct answer.
a. 4.75 hours
b. 6.25 hours
c. 5.75 hours
d. 5.25 hours
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
x= Number of hours carpenter worked
y= Number of hours apprentice worked

1 x + 1 y = 10 .............1
Total value
42 x + 24 y = 325 1/2 .............2
Eliminate y
multiply (1)by -24
Multiply (2) by 1
-24 x -24 y = -240
42 x + 24 y = 325 1/2
Add the two equations
18 x = 85 1/2
/ 18
x = 4 3/4
plug value of x in (1)
1 x + 1 y = 10
4 3/4 + y = 10
y = 10 -4 3/4
y = 5 1/4
y = 5 1/4
x= 4 3/4 Number of hours carpenter worked
4.75 hours
m.ananth@hotmail.ca