Ryan School had 460 students and Zeph School had 30% less students. When an equal number of students joined each school, the ratio of the students in Zeph School to that in Ryan School became 5 : 4. How many students were there in both schools in the end?

	Ryan School	Zeph School	Difference
Before	460		138
Change	+ ?	+ ?
After	5 u	4 u	1 u

Since an equal number of students joined each school, the difference in the number of students at first and in the end between the 2 schools remains the same.  Make the difference between the number of students in Ryan School and Zeph School at first and in the end the same. 

Difference between the number of students in both schools at first
= 30% x 460
= ³⁰₁₀₀ x 460
= 138

Difference between the number of students in both schools in the end
= 5 u - 4 u
= 1 u

1 u = 138

Total number of students in both schools in the end
= 5 u + 4 u
= 9 u
= 9 x 138
= 1242

Answer(s): 1242