吉姆（Jim）、他的妻子以及他们的孩子去日本北海道旅游。 下表给出了可用于计算他们部分支出的信息。

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.