A high school drama department sold 238 tickets for their performance.An adult ticket cost 6.75. A student ticket cost 3.50. They collected $1,252.25. How many student tickets were sold?

Question

A high school drama department sold 238 tickets for their performance.

o An adult ticket cost $6.75.

o A student ticket cost $3.50.

o The high school drama department collected $1,252.25 in ticket sales.

How many student tickets were sold?

Answer 1

set-up a system of equations

let x= adult tickets, y=student tickets

the system:

A). x+y =238

B). 6.75x+3.56y=1252.25

solve this system:

x=238-y

replace "y" with the above in equation B) to find the number of student tickets sold

6.75(238-y)+3.56y=1252.25

Answer 2

A + S = 238

6.75A + 3.5S = 1252.25 multiply 1st equation by 3.5

3.5A + 3.5S = 833.00 subtract to eliminate one variable

3.25A = 419.25

A = 419.25/3.25 = 129 adults

S=238-129 = 109 students