0

# based on venn diagram

A market researcher investigating preference for 3 brands of beverages coffee, tea and cocoa in Kisumu city gathered the following information. From a sample of 800 consumers, 230 took coffee, 245 took tea and 325 took cocoa. 30 took all three beverages, 70 took coffee and cocoa, 110 took coffee only while 185 took cocoa only.

Required:

i.                    Present the above information in a venn diagram

ii.                  Find the number of customers who took tea only

iii.                Find the number of customers who took tea and coffee only

iv.                Find the number of customers who took none of the beverages.

### 1 Answer by Expert Tutors

Arthur D. | Effective Mathematics TutorEffective Mathematics Tutor
5.0 5.0 (9 lesson ratings) (9)
0
800 consumers
Draw three intersecting circles for your Venn diagram with seven sections:coffee only, tea only, cocoa only,
coffee and tea, coffee and cocoa, tea and cocoa, and all three coffee, tea, and cocoa.
230 took coffee
245 took tea
325 took cocoa
30 took coffee, tea, and cocoa
because of the 30, coffee is now 200, tea is now 215, and cocoa is now 295
70 took coffee and cocoa
because of the 70, coffee is now 130, and cocoa is now 225
110 took coffee only
because of the 110, the other 20(130-110) is in the section for coffee and tea
because 20 is in the coffee and tea section, tea only is now 195
185 took cocoa only
cocoa only was 225 but if it's 185 only, then 40(225-185) is in the cocoa and tea section
if 40 is in the cocoa and tea section, tea only is now 155(195-40)
110(coffee only)+70(coffee and cocoa)+30(all three)+20(coffee and tea)=230 took coffee
155(tea only)+40(tea and cocoa)+30(all three)+20(coffee and tea)=245 took tea
185(cocoa only)+40(cocoa and tea)+30(all three)+70(cocoa and coffee)=325 took cocoa
tea only is 155
tea and coffee only is 20
coffee only is 110
coffee and cocoa only is 70
cocoa only is 185
tea and cocoa only is 40
all three is 30
155+20+110+70+185+40+30=610
800-610=190 took none of the beverages coffee, tea, or cocoa