SOLUTION: in a group of 40 workers, the average (arithmetic mean) salary is $70 a day per worker. If some of the workers earn $65 a day and all the rest earn $90 a day, how many workers ear

Question 888558: in a group of 40 workers, the average (arithmetic mean) salary is $70 a day per worker. If some of the workers earn $65 a day and all the rest earn $90 a day, how many workers earn $65 a day?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the total amount of money earned is 40 * 70 = 2800.

x = number of workers that earn 65 a day.
y = number of workers that earn 90 a day.

65x + 90y = 2800

x + y = 40

in the second equation, solve for y to get y = 40 - x

in the first equation, replace y with 40 - x to get:

65x + 90(40 - x) = 2800

simplify to get:

65x + 3600 - 90x = 2800

simplify to get:

-25x + 3600 = 2800

subtract 3600 from both sides of this equation to get:

-25x = -800

divide both sides of this equation by -25 to get:

x = 32

in the equation of x + y = 40, replace x with 32 to get:

32 + y = 40

solve for y to get y = 8

you have 32 workers who make 65 a day.
you have 8 workers who make 90 a day.

32*65 + 8*90 = 2800

2800 / 40 = 70

solution is good.

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