Solve this algebra question

Question

The school production of​ 'Our Town' was a big success. For opening​ night, 508 tickets were sold. Students paid ​$3.00 ​each, while​ non-students paid ​$5.00 each. If a total of $ 1814.00 was​ collected, how many students and how many​ non-students attended?

Answer 1

If we let x represent the number of student tickets sold and y be the number of non-students tickets sold, then we can write the following 2 equations to solve the problem:

x + y = 508 (Equation for number of tickets)

3x + 5y = 1814 (equation for cost of tickets)

Then use substitution to solve the two equations with two unknowns= 290

x = 508 -y

Substitute this expression for x in the cost equation:

3(508 - y) + 5y = 1814

Solve for y using the distributive property , combining like terms, and inverse operations:

1524 - 3y + 5y = 1814

1524 +2y = 1814

1524 + 2y -1524 = 1814 -1524

2y = 290

2y/2 = 290/2

y= 145 non-student tickets

x = 508 - y OR

x= 508 - 145

x =363 student tickets

To check:

145 * $5 + 363 * $3 = $1814

$725 + $1089 = $1814