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In a group of 60 workers, the average (arithmetic mean) salary is $80 a day per worker. If some of the workers earn $75 a day and all the rest earn $100 a day, how many workers earn $75 a day?

Respuesta :

dwh2o13
Let's let x = the number of workers making $75 per day
Then that would mean (60 - x) would be the number of workers who make $100 per day. 
Now the average salary, which needs to be 80, can be found by adding all the salaries of the 60 workers and dividing by 60.  The following equation can model this problem:
[75x + 100(60 - x)]/60 = 80  simplify the left side of the equation
(-25x + 6000)/60 = 80  multiply both sides by 60
-25x + 6000 = 4800  subtract 6000 from both sides
-25x = -1200  divide both sides by -25
x = 48  recall we set 'x' to equal the number of workers making $75 per day
And there you have it!  Hope this helps.. 

the total number of workers that earn $75 per day is 48 and this can be determined by forming the linear equation in one variable.

Given :

  • In a group of 60 workers, the average (arithmetic mean) salary is $80 a day per worker.
  • If some of the workers earn $75 a day and all the rest earn $100 a day.

Let 'a' be the total number of workers that earn $75 per day. So the total number of workers that earn $100 per day is (60 - x).

According to the given data, the average salary of 60 workers is $80. The mathematical expression that represents this situation is:

[tex]\dfrac{75x + 100(60-x)}{60} = 80[/tex]

Simplify the above expression in order to determine the value of 'x'.

75x + 100(60 - x) = 4800

75x + 6000 - 100x = 4800

1200 = 25x

x = 48

So, the total number of workers that earn $75 per day is 48.

For more information, refer to the link given below:

https://brainly.com/question/21835898

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