During the first day of the concert, the number of student tickets sold was 80 fewer than the number of student tickets sold.On the second day, the number of adult tickets sold decreased by 15 percent while the number of student tickets sold increased by 30 percent.The cost of each adult ticket was $65 while the cost of each student ticket was $32.Given that 1824 tickets were sold on the second day, how much money was collected from the sale of the tickets on the first day.

If there were s student tickets and a adult tickets sold on the first day, then we have

a = s-80
.85a + 1.30s = 1824
a = 800
s = 880

so, on day 1 they took in

65*800 + 32*880 = 80160

To solve this problem, let's go through the given information step by step.

Step 1: Let's assign variables to the unknown values:
Let's call the number of student tickets sold on the first day S1.
Let's call the number of adult tickets sold on the first day A1.

Step 2: Translate the given information into equations:
From the given information, we know that the number of student tickets sold on the first day was 80 fewer than the number of student tickets sold (which we can represent as S2) on the second day. This can be written as:
S1 = S2 - 80

We also know that on the second day, the number of adult tickets sold (which we can represent as A2) decreased by 15 percent and the number of student tickets sold increased by 30 percent. This can be written as:
A2 = A1 - (0.15 * A1) (decrease of 15% in adult tickets)
S2 = S1 + (0.30 * S1) (increase of 30% in student tickets)

Step 3: Use the given information to form another equation:
We are given that the total number of tickets sold on the second day (A2 + S2) is 1824. Therefore, we can write:
A2 + S2 = 1824

Step 4: Solve the equations:
Let's substitute the equations from Step 2 into the equation formed in Step 3 to solve for A1 and S1.

A2 + S2 = 1824
(A1 - (0.15 * A1)) + (S1 + (0.30 * S1)) = 1824 (substituting equations from Step 2)
A1 - 0.15A1 + S1 + 0.30S1 = 1824
0.85A1 + 1.30S1 = 1824 (combining like terms)

Now, substitute the equation S1 = S2 - 80 into the simplified equation above:
0.85A1 + 1.30(S2 - 80) = 1824
0.85A1 + 1.30S2 -104 = 1824
0.85A1 + 1.30S2 = 1928 (combining like terms)

Now, we have two equations:
S1 = S2 - 80
0.85A1 + 1.30S2 = 1928

Step 5: Use substitution to solve for S1:
Substitute equation S1 = S2 - 80 into the equation 0.85A1 + 1.30S2 = 1928:
0.85A1 + 1.30(S1 + 80) = 1928
0.85A1 + 1.30S1 + 104 = 1928
0.85A1 + 1.30S1 = 1824 (subtracting 104 from both sides)

Step 6: Solve for A1:
Now we have:
0.85A1 + 1.30S1 = 1824

Since we're looking for the amount of money collected from the sale of tickets on the first day, we need to calculate the total cost of the tickets sold on the first day. We can calculate this by multiplying the number of adult tickets (A1) by the cost per adult ticket ($65) and the number of student tickets (S1) by the cost per student ticket ($32).

Total cost of tickets on the first day = A1 * ($65) + S1 * ($32)

Finally, substitute S1 = 1824 - A1 (from equation found in Step 5) into the equation above and solve for A1:

Total cost of tickets on the first day = A1 * ($65) + (1824 - A1) * ($32)
Total cost of tickets on the first day = 65A1 + 32(1824 - A1)

Now, you can solve this equation using algebra to find the total amount of money that was collected from the sale of tickets on the first day.