Question

In the following exercises, translate to a system of equations and solve.

Tickets for a baseball game are \(69 for Main Level seats and \)39 for Terrace Level seats. A group of sixteen friends went to the game and spent a total of $804 for the tickets. How many of Main Level and how many Terrace Level tickets did they buy?

Short answer

The number of main level tickets are 6 and number of terrace level tickets are 10.

Step-by-step solution

Step 1. Given Information    

The given data is that Tickets for a baseball game are $69 for Main Level seats and $39 for Terrace Level seats. A group of sixteen friends went to the game and spent a total of $804 for the tickets.

Step 2. Calculation   

Let x be the number of main level tickets and ybe the number of terrace level tickets.

Total number of tickets is 16 that is $x+y=16--\left(1\right)$

The total amount paid for tickets is $804 that can be expressed as role="math" localid="1647688654646" $69x+39y=804--\left(2\right)$

Multiply equation (1) with 39 and write the revised equation.

$$\begin{gathered} 39(x+y)=39\left(16\right) \\ 39x+39y=624--\left(3\right) \end{gathered}$$

Solve the equations (2) and (3) by subtracting equation (3) from equation (2) to find the value of x.

$$\begin{gathered} 69x+39y-39x-39y=804-624 \\ 30x=180 \\ x=6 \end{gathered}$$

Substitute the value of x in equation (1) to find the value of y.

$$\begin{gathered} 6+y=16 \\ y=16-6 \\ y=10 \end{gathered}$$