The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total ticket sales were $1050. How many tickets of each type were sold?
Instructions: Write an equation to model each situation.
Can someone please tell me HOW to do this and WHY each step is taken?
The attendance at a baseball game was 400 people. Student tickets cost $2 and adult tickets cost $3. Total ticket sales were $1050. How many tickets of each type were sold?
1--S + A = 400
2--2S + 3A = 1050
3--2 x (1) yields 2S + 2A = 800
4--Subtract (3) from (2) yieldingA = 250
5--It follows that S = 150
200 student tickets and 200 adult tickets
To solve this problem, you can use a system of equations. Let's break it down step by step:
1. Let's start by defining the variables. Let x represent the number of student tickets sold and y represent the number of adult tickets sold.
2. We have two pieces of information from the problem:
a) The attendance at the baseball game was 400 people. This means that the total number of tickets sold (student + adult) is equal to 400: x + y = 400.
b) The total ticket sales amount to $1050. We know that each student ticket costs $2 and each adult ticket costs $3. So, the equation for the total ticket sales is: 2x + 3y = 1050.
By setting up these equations, we can now solve them simultaneously to find the values of x and y.
3. Now we have a system of two equations:
Equation 1: x + y = 400
Equation 2: 2x + 3y = 1050
We can solve this system of equations using different methods such as substitution, elimination, or graphing.
Let's solve it using the substitution method:
- Solve Equation 1 for x: x = 400 - y
- Substitute this value of x into Equation 2: 2(400 - y) + 3y = 1050
4. Simplify and solve the equation:
Distribute the 2: 800 - 2y + 3y = 1050.
Combine like terms: 800 + y = 1050.
Move 800 to the right side by subtracting: y = 1050 - 800.
Simplify: y = 250.
5. Now that we have the value of y, we can substitute it back into Equation 1 to solve for x:
x + 250 = 400.
Move 250 to the right side by subtracting: x = 400 - 250.
Simplify: x = 150.
6. Therefore, there were 150 student tickets and 250 adult tickets sold at the baseball game.
In summary, we set up a system of equations based on the information given in the problem, and then we solved the system using the substitution method to find the values of x and y. This process ensures that both equations accurately represent the given scenarios and allows us to find the solution.