A book writer intends to sell her books to either Australia or Brazil, and she is planning to use Singapore post office Speedpost service to mail her books. The following table shows the mailing prices and other requirements.

1. Identify the correct mailing costs from the table

An 18 kg parcel falls under the ‘20 kg’ rate.

Australia is in Zone C, so Economy cost = $202.

Brazil is in Zone D, so Economy cost = $282.

2. Calculate the percentage increase compared to Australia

$\text{Percentage increase} = \frac{282-202}{202}\times 100\%$

$= \frac{80}{202}\times 100\%$

$=39.6039\ldots\%$

$\approx 39.6\%$

1. Use the parcel dimension restrictions to find the maximum number of books that can fit

Each book has dimensions $6\text{ mm} \times 128\text{ mm} \times 128\text{ mm}$.

To fit the most books, stack them along the $6\text{ mm}$ thickness.

For $n$ books, the parcel dimensions are
$(6n)\text{ mm} \times 128\text{ mm} \times 128\text{ mm}.$

Largest dimension must not exceed $400\text{ mm}$:
$6n \leq 400$
$n \leq 66.6\ldots$

So the maximum whole number of books is
$n=66.$

2. Check the combined length, width and height condition

For $66$ books, the dimensions are
$396\text{ mm} \times 128\text{ mm} \times 128\text{ mm}.$

Combined length, width and height:
$396+128+128=652\text{ mm}$

Since $652\leq 900$, the parcel satisfies the combined dimension condition.

3. Find the weight of 66 books and identify the correct mailing cost to Australia

Weight of $66$ books:
$66\times 75=4950\text{ g}=4.95\text{ kg}.$

Australia is in Zone C. Since $4.95\text{ kg}$ is up to $5\text{ kg}$, the Speedpost Economy cost is
$\$80.$

4. Calculate the required selling price per book

Mailing cost per book:
$\frac{80}{66}=1.2121\ldots$

Required selling price per book:
$1.80+3.00+\frac{80}{66}=6.0121\ldots$

Since the price is to be given to the nearest ten cents and must be at least enough to earn the intended profit, the lowest suitable selling price is
$\$6.10.$