Most of fuel is on the increase. It has been reported that the price may increase by $17 \%$ . Use the information below to calculate how much more would have to be added to the budget to cover the cost of a $17 \%$ increase in fuel. $\newline$ The one-way distance from Auckland Girls' Grammar School to the Tongariro Alpine crossing is $345 \mathrm{~km}$ . $\newline$ The current fuel prices are $\$ 2.80$ per litre. $\newline$ The school van uses $7$ . $2$ litres of petrol per $100 \mathrm{~km}$ . $\newline$ Auckland Girls' Grammar School has decided to take $24$ students and $4$ staff for the camp. $\newline$ Each school van can fit a maximum of ten people.

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Q. Most of fuel is on the increase. It has been reported that the price may increase by

17 \%

. Use the information below to calculate how much more would have to be added to the budget to cover the cost of a

17 \%

increase in fuel.

\newline

The one-way distance from Auckland Girls' Grammar School to the Tongariro Alpine crossing is

345 \mathrm{~km}

\newline

The current fuel prices are

\$ 2.80

per litre.

\newline

The school van uses

7

2

litres of petrol per

100 \mathrm{~km}

\newline

Auckland Girls' Grammar School has decided to take

24

students and

4

staff for the camp.

\newline

Each school van can fit a maximum of ten people.

Calculate Total Distance: First, calculate the total distance for a round trip from Auckland Girls' Grammar School to the Tongariro Alpine crossing. $\newline$ Total distance = $2 \times$ one-way distance $\newline$ Total distance = $2 \times 345 \, \text{km}$ $\newline$ Total distance = $690 \, \text{km}$
Calculate Fuel Needed: Next, calculate the total amount of fuel needed for the round trip. $\newline$ Fuel needed per $100$ km = $7.2$ litres $\newline$ Total fuel needed = (Total distance / $100$ km) * Fuel needed per $100$ km $\newline$ Total fuel needed = ( $690$ km / $100$ km) * $7.2$ litres $\newline$ Total fuel needed = $6.9 * 7.2$ litres $\newline$ Total fuel needed = $49.68$ litres
Calculate Current Cost: Now, calculate the current total cost of fuel for the round trip. $\newline$ Current fuel price = \$$2$.$80$ per litre$\newline$Total cost of fuel = Total fuel needed $\times$ Current fuel price$\newline$Total cost of fuel = $49.68$ litres $\times$ \$$2.80$$\newline$Total cost of fuel = \$$139.104$
Calculate Price Increase: Calculate the increased cost of fuel after a $17$% price increase.$\newline$Percentage increase = $17\%$$\newline$Increased fuel price = Current fuel price $\times (1 + \text{Percentage increase})$$\newline$Increased fuel price = $(\$2.80) \times (1 + 0.17)$$\newline$Increased fuel price = $(\$2.80) \times 1.17$$\newline$Increased fuel price = $(\$3.276)$
Calculate Cost After Increase: Calculate the total cost of fuel after the price increase.$\newline$Total cost after increase = Total fuel needed $\times$ Increased fuel price$\newline$Total cost after increase = $49.68$ litres $\times$ $\$3.276$$\newline$Total cost after increase = $\$162.7968$
Calculate Additional Cost: Finally, calculate how much more needs to be added to the budget to cover the increased fuel cost.$\newline$Additional cost = Total cost after increase - Total cost of fuel$\newline$Additional cost = $\$162.7968$ - $\$139.104$$\newline$Additional cost = $\$23.6928$