The box office took in a total of $2905 in paid admissions for the highschool musical . adult tickrts cost $8 each and student tickrts cost $3 each .a total of 560 people attended the show . which two equations can be used to solve this problem

Let us assume that the number of adults attending the show = x
he number of students attending the high school musical show = y
Then the two equations that can be used to solve the problem are:
x + y = 560
8x + 3y = 2905
The above mentioned equations can be deduced from all the information's that are already provided in the question. The information's given in the question are:
Total amount collected in paid admissions = $2905
Cost of an adult ticket = $8
Cost of a student ticket = $3
Total number of adults and students that went to see the show = 560.

If you would like to solve this problem, you can calculate this using the following two equations:

a ... the number of adult tickets
s ... the number of student tickets

$2905 = a * $8 + s * $3 ... 2905 = 8 * a + 3 * s
a + s = 560 ... a = 560 - s

2905 = 8 * a + 3 * s
2905 = 8 * (560 - s) + 3 * s
2905 = 8 * 560 - 8 * s + 3 * s
2905 - 8 * 560 = - 5 * s
-1575 = - 5 * s    /(-5)
s = 315

a = 560 - s = 560 - 315 = 245

Result: The box office sold 315 student tickets and 245 adult tickets.

The answer is 6 weeks