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?
Karen Park Holliday We know the total tickets sold = 400.
Let x be the number of adult tickets sold.
That means 400 - x is the number of student tickets.
The revenue from adult tickets will be $3 * x, which we can call 3x.
The revenue from student ticks will be $2 * (400 - x), or 800 - 2x.
The total revenue is $1050, so that means:
3x + (800 - 2x) = 1050.
Removing the parentheses:
3x + 800 - 2x = 1050
Subtracting 800 from both sides:
3x - 2x = 250
Simplifying the left side:
x = 250, which is the number of adult tickets.
400-x = student tickets = 400-250 = 150.
ALWAYS check!
In this case, check the revenue:
3x = 3(250) = 750
2(150) = 300
750 + 300 = 1050. Check!
To solve this problem, we can use a system of equations. Let's represent the number of student tickets and adult tickets sold as "x" and "y" respectively.
The first equation comes from the total number of tickets sold: x + y = 400.
The second equation represents the total ticket sales: 2x + 3y = 1050.
To find the values of x and y, we need to solve this system of equations.
One way to do this is by using the substitution method:
Step 1: Solve the first equation for one variable (x or y) in terms of the other variable. In this case, let's solve for x: x = 400 - y.
Step 2: Substitute the expression for x in the second equation: 2(400 - y) + 3y = 1050.
Step 3: Simplify and solve for y: 800 - 2y + 3y = 1050.
Combine like terms: y = 250.
Step 4: Substitute the value of y back into the first equation to find x: x + 250 = 400.
Subtract 250 from both sides: x = 150.
Therefore, 150 student tickets and 250 adult tickets were sold at the baseball game.