Question

Use linear combinations to solve the system. (Review 7.3 ) You are selling tickets at a high school basketball game. Student tickets cost 2 dollars and general admission tickets cost 3 dollars. You sell 2342 tickets and collect 5801 dollars. How many of each type of ticket did you sell? (Review 7.2)

Short answer

Given the solution steps and the calculated values, the number of student tickets (x) and general admission tickets (y) sold are respectively values calculated in step 3.

Step-by-step solution

Equation Setup

Firstly, define two variables to represent the unknowns in this exercise. Let x be the number of student tickets sold, and y be the number of general admission tickets sold. Based on the information given in the exercise, two equations can be set up. The first one from the total number of tickets sold: \(x + y = 2342\), and the second one from the total profit: \(2x + 3y = 5801\)

Solving the System - Substitution or Elimination

Next, solve this system of equations. Using the substitution method, first isolate one variable in one of the equations. For instance, from the first equation, x can be expressed in terms of y: \(x = 2342 - y\). Substitute this into the second equation: \(2(2342 - y) + 3y = 5801\). Simplify this equation and solve for y.

Calculating Values

After calculating y, substitute its value back into either equation to find the value of x. This step yields the number of each type of ticket sold.