Question

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?

Answer 1

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 `"adult's ticket"` the variable `a` and `"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:

`"7 adult tickets + 5 child tickets = $123"`

`color(blue)(7a + 5c = 123)`

The second parts says that the child's ticket is 6 less than the adult's ticket. "`"6 less"`" mean that we are going to `"subtract"`.

`"child's ticket = adult's ticket - 6"`

`color(blue)(c = a - 6)`

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

`7a + 5c = 123`

`7a + 5(a - 6) = 123`

`7a + 5a - 30 = 123`

`12a - 30 = 123`

`12a = 153`

`a = 12.75`

The adult's ticket is `$12.75`. Now substitute that into these second equation and solve:

`c = a - 6`

`c=(12.75)-6`

`c = 6.75`

The child's ticket costs `$6.75`.