SOLUTION: the average age of 8 men is increased by 2 years when 2 of them whose ages are 21 years and 23 years are replaced by two new men. the average age of two new men is?

Question 425899: the average age of 8 men is increased by 2 years when 2 of them whose ages are 21 years and 23 years are replaced by two new men. the average age of two new men is?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the average of the original 8 men is equal to x

this mans that the sum of their ages divided by the number of men = x

we get S/8 = x

we know that if we subtract (21 and 23) from the sum, and we add the ages of 2 other men, that the average age now becomes (x+2).

formula for this would be:

(S - 44 + y)/8 = (x+2)

y represents the sum of the ages of the 2 new men.

we have 2 equations:

S/8 = x and (S - 44 + y)/8 = (x+2)

if we multiply both sides of each equation by 8, then we get:

S = 8*x and S - 44 + y = 8*(x+2)

Since S = 8*x in the first equation we can susbtitute 8*x for S in the second equation to get:

8*x - 44 + y = 8*(x+2)

We simplify this by removing parentheses to get:

8*x - 44 + y = 8*x + 16

we subtract 8*x from both sides of the equation and we add 44 to both sides of the equation to get:

y = 60

y is the sum of the ages of the 2 new men.

their average age is 60/2 = 30

that should be the answer to your question.

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