admission tickets to a motion picture theater were priced at 4 dollars for adults and 3 dollars for students. If 810 tickets were sold and the total receipts were 2853 dollars, how many of each type of ticket weres sold ?

FINAL ANSWER: 423 tickets sold to adults,
387 tickets sold to students.

SOLUTION:
Let tickets sold to adults: x
tickets sold to students : y

To rewrite equation in terms of x for tickets sold to students:
x + y = 810
y = 810 - x

So: Tickets sold to adults: x at 4 dollars each
Tickets sold to students: 810-x at 3 dollars each

Equation:
4(x) + 3(810-x) = 2,853
4x + 2430 - 3x = 2,853
4x - 3x = 2,853 - 2,430
x = 423

Number of tickets for each type:
Adults = x
= 423 tickets

Students = 810-x
= 810 - 423
= 387 tickets

Add: 423 tickets + 387 tickets = 810 tickets

To check if the total receipts is correct:
4x + 3 (810-x) = 2,853
4 (423) + 3 (387) = 2,853
1,692 + 1,161 = 2,853
2,853 = 2,853