Question

The Science Theater charges $5 for

adult tickets and $3 for student tickets.
Mr. Simon purchased 12 tickets (some
student and some adult) for $54. Write
and solve a system of equations to find
out how many adult tickets and how
many student tickets were purchased.

Please show work!

Answer 1

adult tickets purchased = 9

student tickets purchased = 3

Explanation:

a = # of adult tickets purchased

s = # of student tickets purchased

(1) a + s = 12

(2) $5a + $3s = $54

solve equation (1) for s:

s = 12 - a now substitute this into equation (2) so you have an expression all in terms of a

$5a + $3(12 - a) = $54 solve for a

5a + 36 - 3a = 54

2a = 54 - 36 = 18

a = 18/2 = 9 substitute this into equation (1) and solve for s

9 + s = 12

s = 12 - 9 = 3