Algebra 2 word problem??

Question

A survey of 62 restaurant patrons revealed that only 4 did not like either Mexican,Italian,or Chinese food. However, 18 liked both Italian and Mexican food,16 liked both Italian and Chinese food,and 18 liked both Chinese and Mexican food. If 33 patrons liked Italian food,31 liked Mexican food,and 36 liked Chinese food, how many liked all three types of food?How many like only one type of food?

Help :( confusing

Answer 1

If there are 62 patrons, then 62-4=58 so 58 like some type of food.

Now if we have four variables we will have A=the number who like all foods, X=the number who like Italian only, M=the number who like Mexican Only, and C=the number who like Chinese only.

X=33-18-16+A (You have to add back in the ones that like all because they would be in both the 18 and the 16 and therefore counted twice. So X=A-1. With this same logic, M=A-5, and C=A+2.

58 (the total who like food) = A (the ones who like all three) +(18+16+18 - 3A )(the ones who like at least two foods subtracting out the A which have already counted)+X+M+C

58=A+52-3A+X+M+C. Now if you substiute in the X, M, and C you get, 58=A+52-3A+A-1+A-5+A+2 which simplifies to 58=A+48, which means that A=10.

Then Substitute back in the 10 in the upper equations and you get X=9, M=5, and C=12.

So 10 like all three.
9 liked Italian only, 5 liked Mexican only, and 12 liked Chinese only which means that 26 only like one type of food.

Answer 2

The problem is best solved using a venn diagram. but it is difficult to draw one here.

I let x equals to the number of people who likes all 3.

So I and M only = 18 - x
I and C only = 16 - x
C and M only = 18 - x

To find Italian only we have to subtract
33 - (18-x) - (16-x) - x = x - 1

Mexican only
31 - (18-x) - (18-x) -x = x - 5

Chinese only
36 - (18-x) - (16-x) - x = x + 2

Add all these up it should equals 62 - 4 = 58

x + 48 = 58 x = 10
Ans. 10 likes all three

I only = 9, M only = 5 and C only = 12
total = 26

Answer 3

i dont know...let me ask other people..on a different web..^^