# Devon purchased tickets to an air show for 7 adults and 2 children The total cost was $123. The cost of a child's ticket was$6 less than the cost of an adult's ticket. What is the price of an adult and child ticket?

Apr 6, 2018

The adult's ticket is $12.75 and the child's ticket is $6.75

#### Explanation:

There are two pieces of information here, so we will break them down and make two equations.

I will give $\text{adult's ticket}$ the variable $a$ and $\text{child's ticket}$ the variable $c$.

So we know that Devon purchased $7$ adult's tickets and $5$ child's tickets and the resulting cost was $123 dollars. Let's make thing into an equation: $\text{7 adult tickets + 5 child tickets = $123}$

$\textcolor{b l u e}{7 a + 5 c = 123}$

The second parts says that the child's ticket is 6 less than the adult's ticket. "$\text{6 less}$" mean that we are going to $\text{subtract}$.

$\text{child's ticket = adult's ticket - 6}$

$\textcolor{b l u e}{c = a - 6}$

Okay, know we can substitute that second equation into the first one and solve:

$7 a + 5 c = 123$

$7 a + 5 \left(a - 6\right) = 123$

$7 a + 5 a - 30 = 123$

$12 a - 30 = 123$

$12 a = 153$

$a = 12.75$

The adult's ticket is $12.75. Now substitute that into these second equation and solve: $c = a - 6$$c = \left(12.75\right) - 6$$c = 6.75$The child's ticket costs $6.75.