2. A chicken farmer surveyed his flock with the following results. The farmer ha

Question

2. A chicken farmer surveyed his flock with the following results. The farmer has: 9 fat red roosters 7 thin brown hens 2 fat red hens 18 thin brown roosters 26 fat roosters 6 thin red roosters 37 fat chickens 5 thin red hens

[ Hint: You need a Venn diagram with circles for fat, for male (a rooster is a male, a hen is a female), and for red (assume that brown and red are opposite in the chicken world.)]

How many chickens are:

a.   fat?

b.   red?

c.   male

d.   fat, but not male?

e.   brown, but not fat?

f.    red and fat?

Explanation / Answer

et F=fat, T=thin, M=rooster, H=hen, R=red, B=brown then the regions are:

FMR, FMB, FHR, FHB, TMR, TMB, THR, THB.

9 fat red roosters(male) --> FMR=9
37 fat chickens FMR+FMB+FHR+FHB=37
6 thin red roosters --> TMR = 6
2 fat red hens --> FHR = 2
7 thin brown hens --> THB = 7
5 thin red hens --> THR = 5
26 fat roosters (total) --> FMR+FMB=26
18 thin brown roosters --> TMB = 18

So 6 of the 8 regions are given and the other two can be determined by substituting the givens into
FMR+FMB=26 and FMR+FMB+FHR+FHB=37.
9+FMB=26 so FMB = 17
9+17+2+FHB=37 so FHB = 9

The number of fat chickens is FMR+FMB+FHR+FHB=9+17+2+9=37. This was actually stated inthe problem but the technique above will work for less obvious problems.

The number of red chickens is FMR+FHR+TMR+THR=9+2+6+5=22.

The number of male chickens is FMR+FMB+TMR+TMB=9+17+6+18=50.

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