A shop sells big boxes and small boxes as shown. Raja and Hannah bought the same total number of boxes. Both of them bought some big boxes. Raja bought 37 small boxes while Hannah bought 9 small boxes.

1. Express the number of big boxes each person bought in terms of the total number of boxes.

Let the total number of boxes each person bought be $N$.
Raja bought $37$ small boxes, so he bought $N - 37$ big boxes.
Hannah bought $9$ small boxes, so she bought $N - 9$ big boxes.

2. Determine who bought more big boxes and thus paid more.

Since $N - 9 > N - 37$, Hannah bought more big boxes than Raja. Because big boxes are more expensive than small boxes, Hannah paid more.

3. Calculate the difference in the number of each type of box.

Difference in small boxes = $37 - 9 = 28$
Difference in big boxes = $(N - 9) - (N - 37) = 28$
This means Hannah bought $28$ more big boxes and $28$ fewer small boxes than Raja.

4. Calculate the difference in the amount paid.

Difference in cost per box = $\char36{}35.50 - \char36{}9.80 = \char36{}25.70$
Total difference in amount paid = $28 \times \char36{}25.70 = \char36{}719.60$