Question

Daryl bought 10 adult tickets and 10 children's tickets to a zombie movie for $110. Rick bought 6 adult and 5 children tickets for $63 to the same movie. How much money does each type of ticket cost

Answer 1

Answer:

Adult tickets = $8

Children's tickets = $3

Step-by-step explanation:

Set up a system of equations;

x = adult tickets

y = children's tickets

Daryl's situation;

10x + 10y = 110

Rick's situation;

6x + 5y = 63

Hence the system is;

$\left \{ {{10x+10y=110} \atop {6x+5y=63}} \right.$

To solve by elimination, one has to multiply one of the systems by a number such that when one adds the two systems, one variable gets eliminated. One is then left with an expression that can be solved for the other variable. Finally, one can substitute the value of the other variable back, to find the value of the first variable.

$\left \{ {{10x+10y=110} \atop {6x+5y=63}} \right.$

Multiply Rick's situation by (-2)

$\left \{ {{10x+10y=110} \atop {-12x-12y= -126}} \right.$

Add the two equations;

-2x = -16

Inverse operations;

-2x = -16

/-2     /-2

x = 8

Substitute back in;

10x + 1y = 110

10(8) + 10y = 110

Simplify;

80 + 10y = 110

Inverse operations;

80 + 10y =110

-80          -80

10y = 30

/10    /10

y = 3

x = 8

y = 3