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Need Pre-calculus Help?!

[From: ] [author: ] [Date: 11-09-15] [Hit: ]
Alex can do the job in six days, and Ben can do it in eight days. With assistance from Chris, they finish the job in three days. How much money did Chris get?$33.......
Alex and Ben undertake a job for $800. This amount is to be distributed in proportion to the work done. Alex can do the job in six days, and Ben can do it in eight days. With assistance from Chris, they finish the job in three days. How much money did Chris get?

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Alex's work rate is A =1/6 job/day
Ben's is B=1/8 job/day
(A + B + C) *3 = 1 job
A + B + C = 1/3
1/6 + 1/8 + C = 1/3
C = 8/24 - 4/24 - 3/24 = 1/24 job/day


Alex gets 800 * 1/6*3 = $400
Ben gets 800 * 1/8*3 = $300
Chris gets 800*1/24*7 = $100

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(1/6 + 1/8 + 1/x) * 3 = 1
(1/6 + 1/8 + 1/x) = 1/3
(4/24 + 3/24 + 1/x) = 1/3
(7/24 + 1/x) = 1/3
((7x + 24) / (24x)) = 1/3
7x + 24 = 24x / 3
7x + 24 = 8x
24 = x

800 / 24 =>
200 / 6 =>
100 / 3 =>
$33.33
1
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