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.
To find the number of student and adult tickets sold, we need to set up a system of equations based on the given information.
Let's assume the number of student tickets sold is represented by 's', and the number of adult tickets sold is represented by 'a'.
We are given two pieces of information in the problem:
1. The total attendance at the baseball game was 400 people, so the sum of student and adult tickets sold should add up to 400:
s + a = 400
2. The total ticket sales were $1050. Since each student ticket costs $2 and each adult ticket costs $3, we can calculate the total sales equation:
2s + 3a = 1050
Now we have a system of two equations with two variables. We can solve this system using various methods, such as substitution or elimination.
Let's use the substitution method:
1. Solve the first equation for 's':
s = 400 - a
2. Substitute this value of 's' into the second equation:
2(400 - a) + 3a = 1050
Now, simplify and solve for 'a':
800 - 2a + 3a = 1050
800 + a = 1050
a = 1050 - 800
a = 250
Therefore, 250 adult tickets were sold.
To find the number of student tickets sold, substitute 'a' back into the first equation:
s + 250 = 400
s = 400 - 250
s = 150
Therefore, 150 student tickets were sold.
In conclusion, 150 student tickets and 250 adult tickets were sold at the baseball game.
number of student tickets --- x
number of adult tickets --- 400-x
2x + 3(400-x) = 1050
pretty straightforward to solve for x