A theater is selling tickets for a performance. Mr. Smith purchased 8 senior tickets and 5 child tickets for 136$ for his friends and family. Mr. Jackson purchased 4 senior tickets and 6 child tickets for 96$. What is the price of a senior ticket?

Answer 1

Let \( x \) be the price of a senior ticket and \( y \) be the price of a child ticket. We can set up the following system of equations based on the information provided:

1. From Mr. Smith's purchase: \[ 8x + 5y = 136 \]

2. From Mr. Jackson's purchase: \[ 4x + 6y = 96 \]

Now we can solve this system of equations.

First, we can simplify the second equation. Let's divide the entire equation by 2: \[ 2x + 3y = 48 \quad \text{(Equation 2)} \]

Now we have the system:

1. \( 8x + 5y = 136 \) (Equation 1)
2. \( 2x + 3y = 48 \) (Equation 2)

Next, we'll solve Equation 2 for \( y \): \[ 3y = 48 - 2x \] \[ y = \frac{48 - 2x}{3} \]

Now, substitute this expression for \( y \) into Equation 1: \[ 8x + 5\left(\frac{48 - 2x}{3}\right) = 136 \]

Multiply everything by 3 to eliminate the fraction: \[ 24x + 5(48 - 2x) = 408 \] \[ 24x + 240 - 10x = 408 \] \[ 14x + 240 = 408 \]

Now, isolate \( x \): \[ 14x = 408 - 240 \] \[ 14x = 168 \] \[ x = \frac{168}{14} = 12 \]

Now that we have the price of a senior ticket \( (x) \), we can find the price of a child ticket \( (y) \) by substituting \( x = 12 \) back into Equation 2: \[ 2(12) + 3y = 48 \] \[ 24 + 3y = 48 \] \[ 3y = 48 - 24 \] \[ 3y = 24 \] \[ y = 8 \]

Thus, the price of a senior ticket is \( \boxed{12} \) dollars.