adult tickets to a play are $12 student tickets are only $8 if a theater sells 90 tiickets to a play for a total of $980, how many of each kind of ticket did the theater sell?
Adult: x
Student: y
x + y = 90
12x+ 8y = 980
12x +8(90-x) = 980
12x + 720 -8x = 980
4x = 260
x = 65
y = 25
To solve this problem, we can use a system of equations. Let's assume x represents the number of adult tickets sold and y represents the number of student tickets sold.
According to the problem, the total number of tickets sold is 90, so we have the equation:
x + y = 90 (1)
The revenue from selling adult tickets can be calculated by multiplying the number of adult tickets sold (x) by the price per adult ticket ($12). Similarly, the revenue from selling student tickets can be calculated by multiplying the number of student tickets sold (y) by the price per student ticket ($8). The total revenue from ticket sales is given as $980, so we have the equation:
12x + 8y = 980 (2)
Now, we can solve this system of equations (equations 1 and 2) to find the values of x and y.
One way to solve this system of equations is by substitution:
Step 1: Solve equation (1) for x:
x = 90 - y
Step 2: Substitute the value of x from equation (1) into equation (2):
12(90 - y) + 8y = 980
Step 3: Distribute and simplify:
1080 - 12y + 8y = 980
1080 - 980 = 12y - 8y
100 = 4y
Step 4: Solve for y:
4y = 100
y = 100/4
y = 25
Step 5: Substitute the value of y back into equation (1) to solve for x:
x = 90 - y
x = 90 - 25
x = 65
Therefore, the theater sold 65 adult tickets and 25 student tickets.