the number of students attending the Fall play was 150 more than the number of adults attending. Student tickets cost $3, and adult tickets cost $5. A total of $4730 was collected. How many students attend the play?
What is the equation for this problem?
13x-2=4x+38
535
To solve this problem, we can set up a system of equations based on the given information.
Let's let A represent the number of adults attending the play and S represent the number of students attending the play.
According to the problem, the number of students attending the Fall play was 150 more than the number of adults attending. This can be written as:
S = A + 150 (Equation 1)
We also know that student tickets cost $3 and adult tickets cost $5. The total amount collected from ticket sales was $4730. This can be written as:
3S + 5A = 4730 (Equation 2)
We now have a system of equations:
S = A + 150 (Equation 1)
3S + 5A = 4730 (Equation 2)
To solve this system of equations, we can use the substitution method or the elimination method.
Let's solve by substitution:
Substituting the value of S from Equation 1 into Equation 2:
3(A + 150) + 5A = 4730
Simplifying the equation:
3A + 450 + 5A = 4730
8A + 450 = 4730
Subtracting 450 from both sides:
8A = 4280
Dividing both sides by 8:
A = 535
Now that we have the value of A, we can substitute it back into Equation 1 to find the value of S:
S = A + 150
S = 535 + 150
S = 685
Therefore, there were 685 students attending the Fall play.