Jim, his wife and their child visited Hokkaido, Japan. The tables below give information that can be used to work out some of their expenses.

1. Identify which business class ticket can be redeemed using miles

An adult business class redemption ticket costs $140\,000$ miles.

Jim has $150\,000$ miles, so he can redeem $1$ adult business class ticket.

Cash tax still payable for this redeemed ticket: $115.

2. Add the cash amounts payable for the remaining tickets and tax

They need tickets for Jim, his wife and their child.

After redeeming $1$ adult business class ticket, he pays cash for:

$\text{wife's adult business ticket} = \$5500$

$\text{child business ticket} = \$4000$

Total amount paid:

$5500 + 4000 + 115 = 9615$

1. Convert the total journey time into hours

$4$ hours $9$ minutes

$=4+\frac{9}{60}=4.15\text{ h}$

2. Form and solve an equation for the two stage distances

Let the distance of the first stage be $x$ km.

Then the distance of the second stage is $(x+32)$ km.

Using $\text{time}=\dfrac{\text{distance}}{\text{speed}}$,

$\frac{x}{70}+\frac{x+32}{80}=4.15$

Multiply by $560$:

$8x+7(x+32)=2324$

$8x+7x+224=2324$

$15x=2100$

$x=140$

First stage distance $=140$ km.

Second stage distance $=140+32=172$ km.

3. Find the total distance travelled

Total distance travelled

$=140+172=312\text{ km}$

4. Calculate the fuel cost for the SUV

For a SUV, the combined fuel used is $8.8$ litres per $100$ km.

Fuel used:

$\frac{312}{100}\times 8.8=27.456\text{ litres}$

Fuel cost:

$27.456\times 1.70=46.6752$

So the fuel cost is about $46.68.

5. Calculate the driver hire cost for 10 hours on one day

For $1$ day of hire, the first $8$ hours cost $350.

Additional time:

$10-8=2\text{ h}$

Additional cost:

$2\times 45=90$

Driver hire cost:

$350+90=440$

So the driver hire cost is $440.

6. Compare Jim's payment with the amount required for a 20% tip

Total cost before tips:

$440+46.6752=486.6752$

If Jim included a $20\%$ tip, he should have paid:

$1.20\times 486.6752=584.01024$

This is about $584.01.

But Jim paid only $550.

Since

$550<584.01,$

Jim is not correct.