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.