Question

In a group of students, 50% like tea, 70% like coffee, 10% don't like both and 120 like both. By using Venn diagram, find the total number of students.​

Answer 1

Since 10% like neither, then 90% must like tea(T), coffee(C) or both(B). So what % like both? That % would have to be deducted from both the tea and coffee likers to arrive at tea only (TO), coffee only (CO) and those liking both and the three would have to sum to 90%, since 10% like neither. So whatever % the 120 represents it must be deducted from both the tea and coffee likers. I don’t know how to add graphics but in equation form

50-x + 70-x + x + 10 = 100, 130-x = 100, -x = -30, X = 30%,

120/30% = 400, 50%(T)-30%(B)=20%(TO) or 80, 70%-30%=40% or 160, 30% or 120, and 10% or 40

80+160+120+40=400

Answer 2

Explanation:

50% 70% 10%

like tea like coffee don't like both

100%-10% =90%

like coffee,tea or both

50% + 70% =120% - 90% = 30%

like tea + like coffee = - = like both

LIKE BOTH 30%=`120

means 1%=4

100%=400