Bridge To Algebra 2

Question

The school that Mike goes to is selling tickets to a play. On the first day of ticket sales the school sold 2 adult tickets and 7 child tickets for a total of $107. The school took in $29 on the second day by selling 2 adult tickets and 1 child ticket. Find the price of an adult ticket and the price of a child ticket.

Answer 1

2A + 7C = 107

2A + C = 29

subtract

6C = 78

C = 13

2A + 13 = 29

A = 8

Answer 2

The first step in this problem is to establish your relationships between the numbers. In other words, you need to write an equation to represent the problem. I like to start by defining my variables.

C - price of children's ticket

A - price of adult ticket

T - amount of money that the school made

Now we can write an equation to represent the situation. In this problem, there will actually be two equations because we have the first night of the play and the second night of the play.

First Night: 2A + 7C = $107

Second Night: 2A + 1C = $29

You may notice that I never used the variable T in my equation. The reason for this is, I substituted in the specific values of T ($107 and $29 for the respective nights).

Now, my goal is to solve these equations to find the value of both A and C. Because I am solving for two unknown variables, and have two equations to work from, I am solving a systems of equations. There are a couple of strategies that work to solve these; I am going to use substitution.

The premise of substitution is to solve one of my equations for a variable, and then plug that information into the second equation. This leaves me with only one variable and then I can get the value of that variable. Once I know one variable, I can solve for the other.

1. Solve 2A - C = $29 for C.

This means I get C alone. First I will subtract 2A from both sides. This leaves me with -C = 29 - 2A. Then I must multiply both sides by -1 to get C = -29 +2A or C = 2A - 29.

2. Plug in my value (2A - 29) for C in the second equation.

2A + 7C = $107

2A + 7 (2A - 29) = 107

3. Solve the equation for A.

2A + 7 (2A - 29) = 107 (original equation)

2A + 14A - 203 = 107 (multiply the 7 through)

-12A - 203 = 107 (group like terms)

-12A = 107 - 203 = -96 (subtract 203 from both sides)

A = 8 (divide both sides by -12)

This means that the adult ticket cost $8.

4. Use our knowledge of A to solve for C.

2A + 1C = $29

2(8) + C = $29 (plug in 8 for A)

16 + C = $29 (multiplication)

C = 13 (subtract 16 from both sides)

This means that children's tickets cost $13.

Answer: Adult tickets cost $8 and children's tickets cost $13. This isn't the most conventional ticketing price, but if you check by substituting our values into the first equation, the math is correct.