Rebecca always travels by taxi to work. To get a taxi, she has two options. She can either flag down a taxi at the roadside, or book one via a mobile app. The fare calculation for each option is as shown below. Option 1: Flag down a taxi at the roadside.

1. Calculate the distance charge before waiting time and surcharge.

First $1\text{ km}$ charge: $3.20

Distance after first $1\text{ km}$ up to $10\text{ km}$:
$10-1=9\text{ km}=9000\text{ m}$
$9000\div450=20$
Charge $=20\times\char36{}0.22=\char36{}4.40$

Distance after $10\text{ km}$:
$17-10=7\text{ km}=7000\text{ m}$
$7000\div350=20$
Charge $=20\times\char36{}0.22=\char36{}4.40$

2. Calculate the waiting-time charge.

Waiting time $=6\text{ min}=360\text{ s}$

$360\div45=8$

Waiting-time charge $=8\times\char36{}0.22=\char36{}1.76$

3. Add the 25% Monday morning surcharge to get the total cost.

Metered fare:
$\$3.20+\$4.40+\$4.40+\$1.76=\$13.76$

Since Rebecca gets into the taxi by $0730$ on Monday, the weekday morning surcharge is $25\%$ of the metered fare.

Surcharge:
$25\%\times\$13.76=\$3.44$

Total cost:
$\$13.76+\$3.44=\$17.20$

1. Find the number of working weekdays in August 2021 and identify the public holiday.

From the calendar, the weekdays in August 2021 are:

$5$ Mondays, $5$ Tuesdays, $4$ Wednesdays, $4$ Thursdays and $4$ Fridays.

Total number of weekdays
$=5+5+4+4+4=22$

Since $9$ August is a Public Holiday, there are
$22-1=21$
ordinary weekdays and $1$ public holiday weekday.

2. Use the Option 1 cost from part (a) for an ordinary weekday morning, and find the Option 1 cost on the public holiday.

From part (a), the cost for Option 1 on an ordinary Monday morning is
$\$17.20$

This includes a $25\%$ surcharge. Hence the metered fare before surcharge is
$\frac{17.20}{1.25}=13.76$

On $9$ August, a Public Holiday, the Monday--Friday morning surcharge does not apply.

So Option 1 cost on $9$ August is
$\$13.76$

3. Calculate the Option 2 fare using a current booking.

For Option 2,

Base fare $=\char36{}2.80$

Distance fare
$=17\times 0.50=\$8.50$

Time fare
$=25\times 0.15=\$3.75$

Current booking fee $=\char36{}3.30$

Fare before discount
$=2.80+8.50+3.75+3.30=\$18.35$

Since this exceeds $\char36{}10.00$, Rebecca gets a $20\%$ discount.

Option 2 cost
$=80\%\times 18.35=0.8\times 18.35=\$14.68$

4. Choose the cheaper option for each type of weekday and calculate the minimum monthly budget.

For each ordinary weekday:

Option 1 costs $\char36{}17.20$, while Option 2 costs $\char36{}14.68$.

So choose Option 2 for the $21$ ordinary weekdays.

For $9$ August:

Option 1 costs $\char36{}13.76$, while Option 2 costs $\char36{}14.68$.

So choose Option 1 for $9$ August.

Minimum budget
$=21(14.68)+13.76$
$=308.28+13.76$
$=\$322.04$