SOLUTION: a survey of 100 school children was taken to determined how they liked their ice cream. it was found out that 55 like vanilla, 50 do not liked chocolate, 15 like neither chocolate

Question 939622: a survey of 100 school children was taken to determined how they liked their ice cream. it was found out that 55 like vanilla, 50 do not liked chocolate, 15 like neither chocolate nor strawberry ,90 like at least 1 of these flavors, 35 like chocolate and vanilla , 10 like all these flavors, 45 do not like strawberry
find:a. how many of the 100 school children who are surveyed like strawberry only?b. how many like both strawberry and chocolate?c.how many like chocolate only?
Please help
Found 2 solutions by 428225, mathmate:
Answer by 428225(90) (Show Source): You can put this solution on YOUR website!
This is the Venn Diagram of the information provided.

C stands for Chocolate, S for Strawberry & V for Vanilla.
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Now the answers to your questions are
a) 20
b) 20
c) 5
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

This problem is best solved using a Venn Diagram.
The complete solution will not show how the logic works, so here I have a blank Venn diagram, in which
V=vanilla
C=chocolate
S=strawberry
and small numbers represent the order in which the quantity (number of students) are filled.

I suggest you draw the same on paper and fill in the numbers as we go along. Be sure to follow the logic behind the calculations.

Note that it is given that the total number of students is 100, so at the end, you are advised to add up the number of students with all preferences and they should have a sum of 100.

step 1: 10 like all flavours, so space 1 = 10 (V and C and S)
step 2: 90 like at least one, that means 10 like none. space 2 = 100-90 = 10
step 3: 35 like both chocolate and vanilla, that includes the 10 obtained in step 1,so space 3 = 35-10 = 25.
step 4: 15 like neither chocolate nor strawberry, means they either like vanilla, or nothing at all (10). That leaves space 4 = 15-10 = 5.
step 5: 55 like Vanilla, so space 5 = 55-10-25-5 = 15
step 6: 50 don't like chocolate, means they like either Vanilla, strawberry, or none. So space 6 = 50 - 10 -5 -15 = 20
step 7: 45 don't like strawberry means they like either vanilla, chocolate or none. So space 7 = 45 -5 -25 -10 = 5
step 8: the remaining space 8 can be found by the fact that all students add up to 100, so space 8 = 100-10 -5 -25 -15 -10 -5 -20 = 10

This will complete the Venn diagram.
After completing, check that all given criteria are correct.
With the completed and checked Venn diagram in hand, you should have no problem answering the given questions.

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