Question

Two families went to Rollercoaster World.

The Brown family paid $170 for 3 children and 2 adults.
The Peckham family paid $360 for 4 children and 6 adults.

If \displaystyle xx is the price of a child ticket in dollars and \displaystyle yy is the price of an adult ticket in dollars, write a system of equations that models this situation and then solve it to find out how much each type of ticket costs.

Answer 1

Children ticket cost $30 and adult ticket costs $40.

Explanation:

Given that:

x = price of a child ticket

y = price of an adult ticket

According to given statement;

3x+2y=170 Eqn 1

4x+6y=360 Eqn 2

Multiplying Eqn 1 by 3

3(3x+2y=170)

9x+6y=510 Eqn 3

Subtracting Eqn 2 from Eqn 3

(9x+6y)-(4x+6y)=510-360

9x+6y-4x-6y=150

5x=150

Dividing both sides by 5

`(5x)/(5)=(150)/(5)\\x=30`

Putting x=30 in Eqn 1

3(30)+2y=170

90+2y=170

2y = 170-90

2y = 80

Dividing both sides by 2

`(2y)/(2)=(80)/(2)\\y=40`

Hence,

Children ticket cost $30 and adult ticket costs $40.