Question 36: The number of students in four blocks \(6,7,8,9\) is proportional to the numbers \(9; 8; 7; 6\). Knowing that the number of students in class \(9\) is less than the number of students in class \(7\) is \(70\) students. Calculate the number of students in grade 9?

Let the number of students in four grades \(6, 7, 8, 9\) in the order \(x, y, z, t\) (\(x,y,z,t \in {\mathbb N^*) }\) )

According to the problem we have: \(\dfrac{x}{9} = \dfrac{y}{8} = \dfrac{z}{7} = \dfrac{t}{6}\) and \(y – t = 70\).

Applying the property of the series of equal ratios, we get:

\(\dfrac{x}{9} = \dfrac{y}{8} = \dfrac{z}{7} = \dfrac{t}{6} = \dfrac{{y – t}}{{8 – 6}} = \dfrac{{70}}{2} = 35\)

Therefore:

\(x = 9.35 = 315\)

\(y = 8.35 = 280\)

\(z = 7.35 = 245\)

\(t = 6.35 = 210\)

So the number of students in four blocks \(6, 7, 8, 9\) in the order is \(315;280;245;210\).