a group of women sell yam,plantain and maize.10 sell yam,12 sell maize,and 14 sell plantain.5 women sell plantain,4 sell yam and maize,2 sell yam and plantain and 3 sell all.how many women are there?

Emmyrosh

4 years ago

Let the three items be M, Y and P.
n{M ∩ Y} only = 4-3 = 1
n{M ∩ P) only = 5-3 = 2
n{ Y ∩ P} only = 2
n{M} only = 12-(1+3+2) = 6
n{Y} only = 10-(1+2+3) = 4
n{P} only = 14-(2+3+2) = 7
n{M∩P∩Y} = 3
Number of women in the group = 6+4+7+(1+2+2+3) as above =25 women.

Robert01

4 years ago

2 + 3 + x + 5= 14

x= 14 – 10= 4

2 + 3 + 4 + z= 10

z= 10 – 9= 1

4 + 3 + x + y= 12

7 + 4 + y= 12

y= 12 – 11= 1

Total women= 1 + 2 + 3 + 4 + 5 + 4 + 1= 20.