The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B ?  Choices
A) 29/12 B) 59/10 C) 65/8 D) 48/5 E) 29/3
Ratio in A: 4/5 so total students in A = 9x   Ratio in B: 3/17 so total students in B = 20y   (4x+3y)/(5x+17y) = 5/7   solving, x/y = 64/3   required ratio = 9x/20y = (64*9)/(3*20) = 48/5   ANSWER:48/5
<result>D</result>
The only people in each of rooms A and B are students, and each student in each of rooms A and B is either a junior or a senior. The ratio of the number of juniors to the number of seniors in room A is 4 to 5, the ratio of the number of juniors to the number of seniors in room B is 3 to 17, and the ratio of the total number of juniors in both rooms A and B to the total number of seniors in both rooms A and B is 5 to 7. What is the ratio of the total number of students in room A to the total number of students in room B ?