Question

The only people in an auditorium are sophomores, juniors, and seniors. the ratio of the number of sophomores to the number of juniors in the auditorium is 4 to 3. the ratio of the number of juniors to the number of seniors in the auditorium is 5 to 7. the total number of people in the auditorium is 448. how many juniors are in the auditorium?

Answer 1

let
x-------> the number of sophomores
y-------> the number of juniors
z------> the number of seniors

we know that
x/y=4/3-----> x=(4/3)y------> equation 1
y/z=5/7------> z=(7/5)y------> equation 2
x+y+z=448-------> equation 3

substitute equation 1 and equation 2 in equation 3
(4/3)y+y+(7/5)y=448-----> multiply by 15 both sides
20y+15y+21y=6720
56y=6720
y=120

the answer is
the number of juniors is 120