SOLUTION: Hello, I have a test tomorrow and I am stuck on a problem: There are 80 workers with an average salary of 5500. There are 3 set salaries, 5100, 5400 and 5700. 10 workers ge

Question 1029037: Hello,
I have a test tomorrow and I am stuck on a problem:
There are 80 workers with an average salary of 5500.
There are 3 set salaries, 5100, 5400 and 5700.
10 workers get 5100. How many get 5700?
I know that the answer is 50 but I am not sure how they got it.
Thanks.

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The total salary is mean* number or 80*5500=440,000
10 workers get 5100, so that is 51,000 removed
the other 70 get one of two salaries
x+y=70; x gets 5400, y gets 5700
5400x+5700y=389,000, or what is left over.
54x+57y=3890
x+y=70
-54x-57y=-3890, negating everything
54x+54y=3780, multiplying the first by 54. Now we can add them
-3y=-110
This doesn't give an integer.
50 can't be the right answer:
10@5100=51,000 total
50@5700=285,000 total
20@5400=108,000 total
That adds to 444,000, not 440,000
If the average salary were 5550 the answer would be 50. As it stands here, there is no integer answer.

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