Question 503738
With work problems you always determine the amount of work each type of resource can do per day.
Then add up the fractions total 1 whole job.
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m = work done by a man per day
b = work done by a boy per day
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(2m + 5b) * 4 = 1 whole job
(4m + 4b) * 3 = 1 whole job
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8m + 20b = 1
12m + 12b = 1
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adjust the equations to solve using elimination
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3(8m + 20b) = 3
5(12m + 12b) = 5
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24m + 60b = 3
60m + 60b = 5
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-36m = -2
m = 1/18
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So each man does 1/18 of the whole job per day.
Therefore, one man would take 18 days to do the job.
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Either repeat this process or use substitution to find the boys' rate of work.
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(2m + 5b) * 4 = 1
(2/18 + 5b) = 1/4
5b = 1/4 - 2/18
5b = 1/4 - 1/9
5b = 9/36 - 4/36
5b = 5/36
b = 1/36
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So each boy does 1/36 of the whole job per day.
Therefore, one boy would take 36 days to do the job.
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Always check your work.
Substitute these values into one of the equations to check.
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(2m + 5b) * 4 = 1 whole job
(2/18 + 5/36) * 4 = ??
(4/36 + 5/36) * 4 = ??
9/36 * 4 = 36/36 = 1
Correct. 
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Done.