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?

1 Answer
Apr 6, 2018

Answer:

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#.