Help maths problem?
The mean age of combined group of men and women is 30 years. If the mean of the age of men and women are respectively 32 and 27 then the percentage of women in this group? Please can you explain also?
The mean age of combined group of men and women is 30 years. If the mean of the age of men and women are respectively 32 and 27 then the percentage of women in this group? Please can you explain also?
Comments
let x = total combined ages of men
let m = number of men
x/m = 32
x = 32m
let y = total combined ages of women
w = number of women
y/w = 27
y = 27w
(x + y) / (m + w) = 30
x + y = 30(m + w)
x + y = 30m + 30w
32m + 27w = 30m + 30w
2m = 3w
2 / 3 = w / m
ratio of women to men is 2:3
women are 2 / (2 + 3)
women are 2/5 of the group
40%
Mmm...
(x+y)/2 = 30
x/m = 32
y/n = 27
Since it is average...lets assume each woman is 27 years old (the average) and each man is 32 years old. What combination would lead to a 30 year - old total average? Since the average of one man + one woman would be less than 30, we need more men and less women.
Guess and check time!
32 + 2(27)
nope
2(32) + 3(27)
Nope, 27 must be multiplied by an even number
4(27) + 32
The average of THAT is 28, so we need more men in here...
wait. why are we doing guess and check?! Lets try algebra
-Painful
(w(27) + m(32))/w+m= 30
uhhh
umm
well
Okay back to guess and check (well you asked to explain/show work...here it is...)
6(27) + 4(32)
Nope
We need less women and more men, remember?
4(27) + 6(32)?
108 + 192 = 300
300/10 = 30!
So...women are 40% of the group!
Whew that was easy
Let m = men and w = women
m = 1 - w
27w + 32m = 30(m+w)
27w + 32(1 -w) = 30(1-w + w)
-5w + 32 = 30
w = .4 or 40%
The mean age of combined group of men and women is 30 years.
If the mean of the age of men and women are respectively 32 and 27
then the percentage of women in this group?
32m + 27w = 30(m + w)
30m + 30w = 32m + 27w
3w = 2m
The percentage of women in this group is 40.