The school production of 'Our Town' was a big success. For opening night, 497 tickets were sold. Students paid $2.50 each, while non-students paid $4.50 each. If a total of $ 1450.50 was collected, how many students and how many non-students attended?
To find the number of students and non-students who attended the school production, we can set up a system of equations.
Let's assume the number of students who attended the production is "S" and the number of non-students is "N".
According to the given information:
1) The total number of tickets sold is 497, so we have the equation S + N = 497.
2) The total amount collected from ticket sales is $1450.50, so we have the equation 2.50S + 4.50N = 1450.50.
We can solve this system of equations to find the values of S and N.
Using the substitution method, we can solve for S in terms of N in the first equation:
S = 497 - N.
Now, substitute this expression for S in the second equation:
2.50(497 - N) + 4.50N = 1450.50.
Multiply out the terms and simplify the equation:
1242.50 - 2.50N + 4.50N = 1450.50.
2N = 1450.50 - 1242.50.
2N = 208.
N = 104.
Now substitute the value of N back into the equation S = 497 - N to find S:
S = 497 - 104.
S = 393.
Therefore, 393 students and 104 non-students attended the school production of "Our Town".
So, what did they tell you?
s+n = 497
2.50s + 4.50n = 1450.50
Now just solve for s and n.