a) Total vehicles → 125 + 3p + 2q + 20
= 145 + 3p + 2q

Ratio of motorcyles is to total number of vehicles → 3 : 40

3p / (145 + 3p +2q) = 3 / 40
120p = 435 + 9p + 6q
111p – 6q  = 435

b) Ratio of buses is to total number of vehicles → 1 : 10

20 / (145 + 3p + 2q) = 1 / 10
200 = 145 + 3p + 2q
3p + 2q = 55

c) 111p – 6q  = 435 — (1)
3p + 2q = 55 — (2)

(2) × 3: 9p + 6q = 165 — (3)

(1) + (3): 120p = 600
p = 5

Sub p = 5 into (2):
15 + 2q = 55
2q = 40
q = 20

Answer for part a and part b is wrong. 

Correct answer:

a) 37p-2q-145=0

b) 3p+2q-55=0

They’re correct. For part a) I did not reduce it to the simplest form but it’s not needed. The two equations are the same.

For part B, it is the exact same equation with just the 55 shifted over.

To clarify, there are many ways to express the same equation. You need the equations in part a) and b) to solve for part c). So if part a) and b) are wrong, I wouldn’t be able to arrive at the correct answer.