The mean age of 12 women in an office is 35 years old. The mean age of 8 men in an office is 31 years old. What is the mean age (nearest year) of all the people in the office?

34

Step-by-step explanation:

μ₁ = mean age of women

w = age of women

wₙ = number of women

μ₂ = mean age of men

m = age of men

mₙ = number of men

∑w = sum of the ages of all the women

∑m = sum of the ages of all the men

∑(w + m) = sum of the ages of all men and women

μ₀ = mean age of all people in the office

(w + n)ₙ = number of men and women

Formula for mean:

μ₀ = ∑(w + m)/(w + m)ₙ

Sum of the ages of everyone divided by the number of people

∑(w + m) = ∑w + ∑m

μ₁ = 35

wₙ = 12

∑w = 35 × 12

= 420

μ₂ = 31

mₙ = 8

∑m = 31 × 8

= 248

∑(w + m) = 420 + 248

= 668

(w + m)ₙ = wₙ + mₙ

(w + m)ₙ = 12 + 8

= 20

μ₀ = ∑(w + m)/(w + m)ₙ

μ₀ = 668/20

μ₀ = 33.8 → 34 (to the nearest year)