Adult tickets to a concert cost $15 and student tickets cost $12. A total of 300 tickets are sold, and the total receipts were $4140. Write and solve a system of equations to find how many student tickets were sold.
a+c = 300
15a+12c = 4140
Now work your magic.
Which variables are x and y like I need to know if a is x or c is y
??? !!!
there is no x and y
a = adult
c = child
you don't always need x and y to solve equations.
To solve this problem, we can set up a system of equations.
Let's assume "x" represents the number of adult tickets sold and "y" represents the number of student tickets sold.
From the given information, we know that the total number of tickets sold is 300. So, our first equation is:
x + y = 300 -- Equation (1)
The second equation can be derived from the total receipts. Since adult tickets cost $15 and student tickets cost $12, the total amount collected from adult ticket sales would be 15x, and the total amount collected from student ticket sales would be 12y. Given that the total receipts were $4140, our second equation is:
15x + 12y = 4140 -- Equation (2)
Now, we can solve the system of equations (1) and (2) to find the values of x and y.
First, let's multiply equation (1) by 12 to eliminate the y term:
12x + 12y = 3600
Next, we can subtract this equation from equation (2) to eliminate the y term:
(15x + 12y) - (12x + 12y) = 4140 - 3600
3x = 540
Dividing both sides by 3 yields:
x = 180
Now, substitute the value of x into equation (1) to find y:
180 + y = 300
y = 300 - 180
y = 120
Therefore, 120 student tickets were sold.