Question

You are selling tickets for a high school play. Student tickets cost \(\$ 4\) and general admission tickets cost \(\$ 6 .\) You sell 525 tickets and collect \(\$ 2876 .\) How many of each type of ticket did you sell?

Short answer

The number of student tickets sold is 137 and the number of general admission tickets sold is 388.

Step-by-step solution

Define the Variables

Let's denote the number of student tickets as \(x\) and the number of general admission tickets as \(y\).

Formulate the Equations

Now formulate two equations based on the problem. From the total number of tickets we have: \(x + y = 525\). From the total amount of money collected we have: \(4x + 6y = 2876\).

Solve the Equations

This is a system of two equations with two variables. Start by multiplying the first equation by 4 to make the coefficient of \(x\) in both equations equal. This gives us: \(4x + 4y = 2100\). Next, subtract this new equation from the second equation: \(4x + 6y - (4x + 4y) = 2876 - 2100\), simplifying gives: \(2y = 776\). Dividing by 2 gives \(y = 388\). Substitute \(y = 388\) into the first equation: \(x + 388 = 525\). By subtracting 388 from both sides, we find \(x = 137\).

Verify the Solution

Verify the answer by substituting \(x = 137\) and \(y = 388\) into both original equations to make sure they hold true.