SOLUTION: A survey of 40 shoppers found that 12 like Crunchy Cereal and 23 like Wheat Cereal. Twice as many dislike both brands as like both brands. How many shoppers like both brands?

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A survey of 40 shoppers found that 12 like Crunchy Cereal and 23 like Wheat Cereal. Twice as many dislike both brands as like both brands. How many shoppers like both brands?      Log On


   

Question 2326: A survey of 40 shoppers found that 12 like Crunchy Cereal and 23 like Wheat Cereal. Twice as many dislike both brands as like both brands. How many shoppers like both brands?
Answer by khwang(438) About Me  (Show Source):
You can put this solution on YOUR website!
Let CC be the set of shoppers like Crunchy Cereal and
let WC be the set of shoppers like Wheat Cereal.
then |CC|,|WC| are the size (cardinality) of the two sets.
Assume x shoppers like both cereal(CC & WC).
We have x = number of intersection of CC & WC.
Total = |CC U WC| + number of shoppers dislike both brands
(union)
Since |CC U WC| = |CC| + |WC| - x = 12 + 23 -x = 35 - x,
and number of shoppers dislike both brands = 2x.
Hence, 40 = 35-x + 2x = 35 + x.
So, x = 5 shoppers like both brands.
Kenny