Ms Wong received $6120 from selling some bags and some dresses.
She received $3240 more for the bags than the dresses. 4 times as many bags as dresses were sold. Each dress cost $15 more than each bag.

1. Use the sum and difference of the amounts received to find the amount received for the bags.

Let the amount received for the bags be $B$ and for the dresses be $D$.
We know:
$B + D = 6120$
$B - D = 3240$
Adding the two equations:
$2B = 6120 + 3240 = 9360$
$B = 9360 \div 2 = 4680$

1. Find the total amount received for dresses and bags.

Amount for dresses = $\frac{\char36{}6120 - \char36{}3240}{2} = \char36{}1440$
Amount for bags = $\char36{}1440 + \char36{}3240 = \char36{}4680$

2. Express the cost of each dress and each bag in terms of the number of dresses.

Let the number of dresses sold be $x$.
Then the number of bags sold is $4x$.
Cost of each dress = $\frac{1440}{x}$
Cost of each bag = $\frac{4680}{4x} = \frac{1170}{x}$

3. Form an equation using the given price difference and solve for $x$.

$\frac{1440}{x} - \frac{1170}{x} = 15$
$\frac{270}{x} = 15$
$x = \frac{270}{15} = 18$