At a concert, $9180 was collected from the sale of adult and child tickets. The ratio of the money collected from adult to child tickets is 14 : 3. $\frac{1}{5}$ of the tickets sold were child tickets. Each adult ticket is $9 more than each child ticket. How many child tickets were sold? Ans: ___

1. Find the total money collected from adult and child tickets respectively.

Total units for money = $14 + 3 = 17$
$17 \text{ units} = \char36{}9180$
$1 \text{ unit} = \char36{}9180 \div 17 = \char36{}540$
Money from adult tickets = $14 \times \char36{}540 = \char36{}7560$
Money from child tickets = $3 \times \char36{}540 = \char36{}1620$

2. Determine the ratio of the number of adult tickets to child tickets.

Fraction of child tickets = $\frac{1}{5}$
Fraction of adult tickets = $1 - \frac{1}{5} = \frac{4}{5}$
Ratio of number of adult tickets to child tickets = $4 : 1$

3. Express the price of each ticket type in terms of units and find the number of child tickets.

Let the number of child tickets be $1u$ and adult tickets be $4u$.
Price of a child ticket = $\frac{1620}{1u}$
Price of an adult ticket = $\frac{7560}{4u} = \frac{1890}{1u}$
Difference in price = $\frac{1890}{1u} - \frac{1620}{1u} = \frac{270}{1u}$
We are given that the difference is $\char36{}9$.
$\frac{270}{1u} = 9$
$1u = 270 \div 9 = 30$
Number of child tickets = $30$