# 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

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