The drama club is putting on a performance Saturday night. They sell students tickets for $5 and adult tickets for $7. They make a total of $2450.

Question

Define your variables and write an equation in standard form that models the number of students and adults that attended the performance.

Answer 1

5S+7A=2450

S equals the number of student tickets sold, A= the number of adult tickets sold

You can graph this as a straight line, with S on the vertical axis and A on the horizontal axis

y intercept = 2450/5 = 490, x intercept = 2450/7 =350. Those are the maximum number of student or adult tickets that could have been sold. Connect those 2 intercepts with a straight line and any points with integers (A,S) are solutions to the problem.

Usually this type of problem adds a 2nd constraint, the total number of tickets sold.

without that, you get multiple solutions. IF A and S were not required to be integers, you would get an infinite number of solutions.

to get 0 as the last digit for total sales, A has to end in a zero or a 5, such as 300. 300A=2100, then S =350/5 =70

if A = 200, 200A = 1400 and S=2050/5 = 410

Pick any A that ends in a 0 or 5 and there's an S that will also be an integer.

A =10, S=(2450-70)/5 = 2380/5 = 476

A=5 S =(2450-35)/5 =2415/5 = 483

There are about 70 solutions

Answer 2

Let s = number of student ticket sold

Let a = number of adult tickets sold

5s + 7a = 2450

We need more information to solve for s and a.

I hope this helps. If you have any questions please contact me.