At the out-rage concert, 723 tickets were sold for $3/student and $5/nonstudent. the benefit raised $2815. How many non-student tickets were sold
number of student tickets --- x
number of adult tickets -----723-x
solve for x ...
3x + 5(723-x) = 2815
-100
Step 1: Let's assume that the number of student tickets sold is 'x'.
Step 2: Since the total number of tickets sold is 723, the number of non-student tickets sold can be calculated as (723 - x).
Step 3: The total amount raised from student tickets is given by x * $3.
Step 4: The total amount raised from non-student tickets is given by (723 - x) * $5.
Step 5: According to the given information, the total amount raised is $2815.
Step 6: Now we can set up an equation using the information from steps 3, 4, and 5:
(x * $3) + ((723 - x) * $5) = $2815
Step 7: We can simplify this equation:
3x + 3615 - 5x = 2815
Step 8: Combining like terms, we get:
-2x + 3615 = 2815
Step 9: Moving the constant term to the right side of the equation:
-2x = 2815 - 3615
Step 10: Simplifying the right side of the equation:
-2x = -800
Step 11: Dividing both sides of the equation by -2:
x = -800 / -2
Step 12: Simplifying the left side of the equation:
x = 400
Step 13: Therefore, the number of non-student tickets sold is (723 - x) = (723 - 400) = 323.
Thus, 323 non-student tickets were sold at the Out-rage concert.
To find the number of non-student tickets sold, we need to set up an equation based on the given information. Let's denote the number of student tickets as "s" and the number of non-student tickets as "n."
Given that the number of student tickets and non-student tickets sums up to 723, we can write the equation:
s + n = 723 ...equation (1)
Additionally, the total amount raised from the concert is $2815. Since each student ticket costs $3 and each non-student ticket costs $5, we can write another equation for the total amount raised:
3s + 5n = 2815 ...equation (2)
Now we have a system of equations (equation 1 and equation 2) that we can solve to find the values of "s" and "n."
There are different methods to solve a system of equations, such as substitution, elimination, or matrix methods. Let's use the substitution method in this case.
From equation (1), we can express "s" in terms of "n":
s = 723 - n
Now substitute this expression for "s" in equation (2):
3(723 - n) + 5n = 2815
Simplify the equation:
2169 - 3n + 5n = 2815
Combine like terms:
2n = 646
Divide both sides by 2:
n = 323
Hence, 323 non-student tickets were sold at the Out-rage concert.