Question

10. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3

and 8 can attend a movie for $15. An adult ticket costs as much as the combined cost of a student ticket
and a child ticket. You purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23.

Answer 1

The ticket prices will as follows:

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Explanation:

Thinking process:

Let the price of the student ticket be $x and the price of a child ticket be $y. An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).

1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then

2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then

Now, solve the system of two equations:

Solve the last equation

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Answer 2

Students ticket = $4

Child ticket = $1

Adult ticket = $5

Explanation:

Let the price of the student ticket be $x and the price of a child ticket be $y. An adult ticket costs as much as the combined cost of a student ticket and a child ticket, so the price of one adult ticket is $(x+y).

1. A movie theater advertises that a family of two adults, one student, and one child between the ages of 3 and 8 can attend a movie for $15. Then

`2(x+y)+x+y=15`

2. If you purchase 1 adult ticket, 4 student tickets, and 2 child tickets for $23, then

`(x+y)+4x+2y=23`

Now, solve the system of two equations:

`\left\{\begin{array}{l}2(x+y)+x+y=15\\ \\(x+y)+4x+2y=23\end{array}\right.\Rightarrow \left\{\begin{array}{l}3(x+y)=15\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}x+y=5\\ \\5x+3y=23\end{array}\right.\\ \\\left\{\begin{array}{l}y=5-x\\ \\5x+3(5-x)=23\end{array}\right.`

Solve the last equation

`5x+15-3x=23\\ \\2x=23-15\\ \\2x=8\\ \\x=4\\ \\y=5-x=5-4=1`

Students ticket = $4

Child ticket = $1

Adult ticket = $5