# 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 ?

2
by jalaine25

2015-09-02T20:43:12+08:00
• Brainly User
2015-09-03T08:48:14+08:00

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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:
= 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