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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