Tickets for a play cost $7 for students and $10 for adults. on opening night, all 380 seats were filled. and the box office revenue was $3290.00. how many student and how many adult tickets were sold?

We can create two equations:

[tex]\sf 7x+10y=3290[/tex]
[tex]\sf x+y=380[/tex]

Where 'x' is the number of student tickets sold and 'y' is the number of adult tickets sold.

Solve the second equation for 'x' and then plug that in for 'x' in the first equation:

[tex]\sf x+y=380[/tex]

[tex]\sf x=380-y[/tex]

Plug in 380 - y for 'x' in the first equation:

[tex]\sf 7x+10y=3290[/tex]

[tex]\sf 7(380-y)+10y=3290[/tex]

Distribute:

[tex]\sf 2660-7y+10y=3290[/tex]

Combine like terms(-7y + 10y = 3y):

[tex]\sf 2660+3y=3290[/tex]

Subtract 2660 to both sides:

[tex]\sf 3y=630[/tex]

Divide 3 to both sides:

[tex]\sf y=\boxed{\sf 210}[/tex]

So there were 210 adult tickets sold. Now plug this into any of the two equations and solve for 'x' to find the amount of student tickets sold:

[tex]\sf x+y=380[/tex]

[tex]\sf x+210=380[/tex]

Subtract 210 to both sides:

[tex]\sf x=\boxed{\sf 170}[/tex]

So there were 170 student tickets sold.