The number of students attending the fall play was 150 more than the number of adults attending. Students tickets cost $3, and adult tickets cost 45 . A total of $4730 was collected. How many students attended the play?
this is what i have, but i need help on the equation.
let x = students let y= adults
x=y+150
x=3x+5y+150
150*3=450, 4730-450=4280, 4280/2=2140
the # of students is 2140+150=2290
4730-150=4
Your second equation is completely wrong. The two equations should be
x = y + 150
3x + 5y = 4730
So, 3(y +150) + 5y = 4730
8y = 4280
Solve for y, then x.
To solve this problem, we can set up the equation based on the given information:
Let's denote the number of students attending the play as 'x' and the number of adults attending as 'y.'
We are told that the number of students attending the play was 150 more than the number of adults attending. Therefore, we can write the equation:
x = y + 150 ---(1)
We also know that student tickets cost $3 and adult tickets cost $45, and a total of $4730 was collected. So, we can write another equation based on the revenue:
3x + 45y = 4730 ---(2)
Now, we can solve these equations simultaneously to find the values of x and y.
We can rearrange equation (1) to express y in terms of x:
y = x - 150
Substituting this expression for y in equation (2), we have:
3x + 45(x - 150) = 4730
Simplifying:
3x + 45x - 6750 = 4730
48x = 11480
x = 11480/48
x ≈ 239.17
Since it doesn't make sense to have a fraction of a student, we can conclude that approximately 239 students attended the play.
Therefore, the number of students attending the play is 239.
To solve this problem, you need to set up a system of equations based on the given information.
Let's let x represent the number of students attending the fall play and y represent the number of adults attending.
From the problem statement, we know that the number of students attending the fall play was 150 more than the number of adults attending. This can be written as:
x = y + 150 (Equation 1)
We also know that the total amount collected from ticket sales was $4730. The cost of each student ticket is $3, so the total amount collected from student tickets is 3x. The cost of each adult ticket is $45, so the total amount collected from adult tickets is 45y. Therefore, we can write another equation:
3x + 45y = 4730 (Equation 2)
Now we have a system of equations:
x = y + 150
3x + 45y = 4730
To solve this system, you can use the substitution method or the elimination method. Let's use the substitution method here.
From Equation 1, we can substitute y + 150 for x in Equation 2:
3(y + 150) + 45y = 4730
Simplifying this equation:
3y + 450 + 45y = 4730
48y + 450 = 4730
48y = 4730 - 450
48y = 4280
y = 4280 / 48
y = 89
Now that we have the value of y, we can substitute it back into Equation 1 to find x:
x = y + 150
x = 89 + 150
x = 239
Therefore, the number of students attending the play is 239.