The average age of 8 men increase by 2 years when two women are included in place of two menof ages 21 and 23 years. Find the average age of the women?
Answers
Answer:
Total age increased = (8 * 2) years = 16 years.
Step-by-step explanation:
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The average of the original 8 men is equal to x
This means 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 substitute 8*x for S in the second equation to get:
8×x−44+y=8×(x+2)
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
is the sum of the ages of the 2 new men.
their average age is 60/2 = 30