Howard School had 316 pupils and Valen School had 25% less pupils. When an equal number of pupils joined each school, the ratio of the pupils in Valen School to that in Howard School became 5 : 4. How many pupils were there in both schools in the end?

	Howard School	Valen School	Difference
Before	316		79
Change	+ ?	+ ?
After	5 u	4 u	1 u

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

Difference between the number of pupils in both schools at first
= 25% x 316
= ²⁵₁₀₀ x 316
= 79

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

1 u = 79

Total number of pupils in both schools in the end
= 5 u + 4 u
= 9 u
= 9 x 79
= 711

Answer(s): 711