Arthur D. answered • 02/23/14

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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