contestada

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.

Respuesta :

absor201

Answer:

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

Step-by-step 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

[tex]\frac{5x}{5}=\frac{150}{5}\\x=30[/tex]

Putting x=30 in Eqn 1

3(30)+2y=170

90+2y=170

2y = 170-90

2y = 80

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{80}{2}\\y=40[/tex]

Hence,

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