Help maths problem?

Comments

• david

  May 2021

  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%
• jeffrey

  May 2021

  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
• steve-a

  May 2021

  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%
• krishnamurthy

  May 2021

  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.