# There are 240 people in a room, the ratio of people who like Iron Man to people who don't like Iron man is 5:3, the ratio of people who like Captain America to the ratio of people who don't like Captain America is 7:5, 86 people like both of those characters, find out how many people dislike both characters

Asked By Atiksh On 01/11/2018 09:19

## Answers

Neil There are 240 people in a room, the ratio of people who like Iron Man to people who don't like Iron man is 5:3, the ratio of people who like Captain America to the ratio of people who don't like Captain America is 7:5, 86 people like both of those characters, find out how many people dislike both characters
TEAM SPECIAL
A = Like Iron Man
B = Dislike Iron Man
C = Like Captain America
D = Dislike Captain America
Given:
A/B = 5/3
C/D = 7/5
(A and C) = 86
n = 240
Unknowns:
A, B, C, D, and (B and D)
Target: (B and D)
Plan: Use the fact that A + C – (A and C) + ( B and D) = n
A/B = 5/3
B = (3/5)*A
A + B = 240
(3/5)*A + A = 240
(3/5)* A + (5/5)*A = 240
A(3/5 + 5/5) =240
A(8/5) = 240
A*(8/5) = 8*30
A = 150
C/D = 7/5
D = (5/7)*C
C + D = 240
C + (5/7)*C = 240
(7/7)*C + (5/7)*C = 240
C(12/7) = 240
C = 140
A + C – (A and C) + ( B and D) = n
150 + 140 – 86 + (B and D) = 240
290 – 86 + ( B and D ) = 240
204 + ( B and D) = 240
(B and D) = 240 - 204
(B and D) = 36

Answered On 01/25/2018 05:07

Answered On 01/25/2018 05:07

Determine the ratio of people who liked a superhero and the people who disliked a superhero to the total number of people. Likes ratio will be likes/(likes+dislikes). Dislikes ratio will be dislikes/(likes+dislikes). For Iron Man likes ratio = 5/(5+3) =5/8, dislikes = 3/(5+3)=3/8. For Captain America: likes ratio = 7/(7+5)=7/12, dislikes = 5/(7+5)=5/12. Multiply each ratio by the total number of people (240). A=people who like Iron Man. B= people who dislike Iron Man. C= people who like Captain America. D= people who dislike Captain America. A=5/8(240)=150. B=3/8(240)=90. C=7/12(240)=140. D=5/12(240)=100. To get the number of people who liked Iron Man and/or Captain America, add A and C. 150+140=290. Subtract the number who liked both from to get the number of people who liked either hero. 290-86=204. Subtract the number of people who liked either from the total number of people to get the number of people who disliked both. 240-204=36

Answered On 02/01/2018 17:06

Answered On 02/01/2018 17:06

Answered On 02/01/2018 17:06

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