Ryan purchased tickets to air show

Question

Ryan purchased tickets to air show for 4 adults and 2 children. The total cost was $86. The cost of a child's ticket was $5 less than the cost of an adults ticket. Find the price of an adults ticket and a child's.

Answer 1

Lets call the cost of 1 adult ticket, x and the cost of 1 child's ticket, y

 

The total cost for 4 adults and 2 children can be written as 4x + 2y = 86  (1)

We know the cost of a child's ticket was $5 less than the cost of an adult's ticket. So: x - y =5  (2)

 

We have two equations and two unknowns, so we can solve for x and y. Let's rearrange equation (2): x = y + 5

Plugging this x value into equation (1): 4*(y+5) + 2y = 86 --> 4y +20 +2y=86 --> 6y= 86-20 --> 6y=66 --> y=11

We can use the new equation (2) to find x: x = y+5 ---> x=11+5= 16.

 

Let's check our answers:

At $16 per ticket for adults and $11 per ticket for children, 4 adult tickets and 2 children tickets would cost:

16 * 4 + 11*2= 64 + 22 = 86

 

The difference between the adult's ticket and the child's ticket is $16 - $11 = $5