Divide 184 into two parts such that one-third of one part may exceed one-seventh of the part by 8. What is the bigger part?

The correct answer is 112

Let the first part be x.
∴ The other part be (184 - x)
One-third of first part = $\frac{x}{3}$
One-seventh of the other part = $\frac{(184 - x)}{7}$
∴ We can form the equation as follows
$\frac{x}{3}$ = $\frac{(184 - x)}{7}$ + 8
∴ $\frac{x}{3}$ = $\frac{(184 - x)}{7}$ + $\frac{(8 * 7)}{7}$
∴ $\frac{x}{3}$ = $\frac{(184 - x) + 56}{7}$
∴ By cross multiplication
x * 7 = 3 ((184 - x) + 56)
or 7x = 3 (240 - x)
∴ 7x + 3x = 720
∴ 10x = 720 or x = 72 and the other part will be 184 - 72 = 112
The bigger part is 112