Using the properties of proportion, solve the following equation for x;

given $\dfrac{x^3 + 3x}{3x^2 + 1} = \dfrac{341}{91}.$

If $\dfrac{x + y}{ax + by} = \dfrac{y + z}{ay + bz} = \dfrac{z + x}{az + bx}$, prove that each of these ratio is equal to $\dfrac{2}{a + b},$ unless x + y + z = 0.

When the number 210 is increased in the ratio 5 : 7, the new number is

1. 150
2. 180
3. 294
4. 420

Two numbers are in the ratio 7 : 9. If the sum of the numbers is 288, then the smaller number is

1. 126
2. 162
3. 112
4. 144