SOLUTION: an employment agency specializing in temporary construction help pays heavy equipment operators $1.20 per day and general laborers $91 per day if thirty-one people were hired and t

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Question 1118379: an employment agency specializing in temporary construction help pays heavy equipment operators $1.20 per day and general laborers $91 per day if thirty-one people were hired and the payroll was $3339 how many heavy equipment operators were employed? how many laborers
Answer by greenestamps(13206) About Me  (Show Source):
You can put this solution on YOUR website!


It would be a good idea for you to look at what you have written before you send your question to us. $1.20 a day for heavy equipment operators? I don't think anybody would take that job.

So the real rate is clearly supposed to be $120 per day. Then we have
x heavy equipment operators at $120 per day and y general laborers at $91 per day, making 31 workers with a total pay of $3339 per day. Then

x%2By+=+31
120x%2B91y+=+3339

Unfortunately, when we try to solve that system of equations, we don't get answers that are whole numbers. So even after correcting your $1.20 per day to $120 per day, there is a flaw in your statement of the problem.

When I first read the problem, it occurred to me that we could solve the problem with logical analysis using only the total pay, without knowing the total number of workers.

Looking at the equation for total pay, we can see that the total pay for the heavy equipment operators will be a multiple of $10. Since the total pay is $3339 and the daily pay for the general laborers is $91, the number of general laborers must be a number ending in 9.

Then we could try 9, 19, 29,... as the number of general laborers and see which gives us a whole number for the number of heavy equipment operators.

But we can be even a little smarter than that. The total pay, $3339, is a multiple of 3, and the daily pay for the heavy equipment operators is a multiple of 3. Since the $91 daily pay for the general laborers is NOT a multiple of 3, the number of general laborers MUST be a multiple of 3.

That means the number of general laborers is either 9, or 39, or 69, or.... With the total pay being $3339, the only number that works is 9.

That gives us 9($91) = $819 for the total pay for the general laborers, leaving $3339-$819 = $2520 as the total pay for the heavy equipment operators. At $120 per day, the number of heavy equipment operators is then $2520/$120 = 21.

So the total number of workers is 9+21 = 30 -- NOT 31, as you say in your statement of the problem.