A 70 seater passenger bus leaves Bamenda for Yaounde, a distance of 400km. The driver pays 5000 FCFA at each toll gate located after every 150km. a. Find the number of toll gates between the two towns

$$
\text{Number of toll gates} = \left\lfloor \frac{\text{Total distance}}{\text{Distance per gate}} \right\rfloor
$$
$$
\text{Number of toll gates} = \left\lfloor \frac{400 \text{ km}}{150 \text{ km}} \right\rfloor
$$
$$
\text{Number of toll gates} = \lfloor 2.66... \rfloor
$$
$$
\text{Number of toll gates} = 2
$$
The number of toll gates is $\boxed{2}$.

$$
\text{Total toll gate cost} = \text{Number of gates} \times \text{Cost per gate}
$$
$$
\text{Total toll gate cost} = 2 \times 5000 \text{ FCFA}
$$
$$
\text{Total toll gate cost} = 10000 \text{ FCFA}
$$
The total amount paid for the toll gates is $\boxed{10000 \text{ FCFA}}$.

$$
\text{Actual passengers} = \text{Total seats} - \text{Reserved seats}
$$
$$
\text{Actual passengers} = 70 - 2
$$
$$
\text{Actual passengers} = 68
$$
The actual number of passengers carried is $\boxed{68}$.

    $$
    \text{Total collected} = \text{Fare per passenger} \times \text{Actual passengers}
    $$
    $$
    \text{Total collected} = 5000 \text{ FCFA} \times 68
    $$
    $$
    \text{Total collected} = 340000 \text{ FCFA}
    $$
    The total amount collected for the fare is $\boxed{340000 \text{ FCFA}}$.

*   **ii. The balance after all the expenditures are made.**

    $$
    \text{Total expenditures} = \text{Toll gate cost} + \text{Fuel cost}
    $$
    $$
    \text{Total expenditures} = 10000 \text{ FCFA} + 100000 \text{ FCFA}
    $$
    $$
    \text{Total expenditures} = 110000 \text{ FCFA}
    $$

    $$
    \text{Balance} = \text{Total collected} - \text{Total expenditures}
    $$
    $$
    \text{Balance} = 340000 \text{ FCFA} - 110000 \text{ FCFA}
    $$
    $$
    \text{Balance} = 230000 \text{ FCFA}
    $$
    The balance after all expenditures is $\boxed{230000 \text{ FCFA}}$.

$$
f(4) = 4 - 3
$$
$$
f(4) = 1
$$
The value of f(4) is $\boxed{1}$.

$$
fg(x) = f(g(x))
$$
$$
fg(x) = f(2x+1)
$$

$$
fg(x) = (2x+1) - 3
$$
$$
fg(x) = 2x - 2
$$
The function fg(x) is $\boxed{2x-2}$.

$$
y = 2x+1
$$

$$
x = 2y+1
$$

$$
x - 1 = 2y
$$
$$
y = \frac{x-1}{2}
$$
The inverse function $g^{-1}(x)$ is $\boxed{\frac{x-1}{2}}$.

$$
3x + 9 = 30
$$

$$
3x = 30 - 9
$$
$$
3x = 21
$$

$$
x = \frac{21}{3}
$$
$$
x = 7
$$
The value of x is $\boxed{7}$.

$$
\text{Students studying neither} = 2 \times 7
$$
$$
\text{Students studying neither} = 14
$$
The number of students who study neither physics nor chemistry is $\boxed{14}$.

$$
\text{Students studying one subject only} = (\text{Students in P only}) + (\text{Students in C only})
$$
$$
\text{Students studying one subject only} = x + 5
$$

$$
\text{Students studying one subject only} = 7 + 5
$$
$$
\text{Students studying one subject only} = 12
$$
The number of students studying one subject only is $\boxed{12}$.