Word Problem

[babybells96]

A theater performance sold 1800 tickets over the weekend. Admission prices were $15 for adults and $9 for students. The total amount collected was $22,800. How many tickets were sold to adults? I am not sure how to begin this problem. I know I am going to have to hold one of the variables constant to figure out how many tickets were sold, but I do not know how to set up the equation. Thank you so much!

 

[pka]

A theater performance sold 1800 tickets over the weekend. Admission prices were $15 for adults and $9 for students. The total amount collected was $22,800. How many tickets were sold to adults? I am not sure how to begin this problem. I know I am going to have to hold one of the variables constant to figure out how many tickets were sold, but I do not know how to set up the equation. Thank you so much!

What about
\(\displaystyle \ a+s=1800\\15a+9s=22800~?\)

 

[mmm4444bot]

I know I am going to have to hold one of the variables constant to figure out how many tickets were sold

The given information tells you how many tickets were sold; that number is 1800.

It's not necessary to assign a constant to one of the variables. You could, but, if you were to do that, finding the answer would involve a lot of guessing and checking, yes?

The direct approach is to write a system of two equations (like the one pka posted for you).

If you need more help (solving for a), please post your work thus far. Cheers :cool:

 

[HallsofIvy]

A theater performance sold 1800 tickets over the weekend. Admission prices were $15 for adults and $9 for students. The total amount collected was $22,800. How many tickets were sold to adults? I am not sure how to begin this problem. I know I am going to have to hold one of the variables constant to figure out how many tickets were sold, but I do not know how to set up the equation. Thank you so much!

I really don't know what "hold one of the variables constant" means!

Let x be the number of adult tickets. Since there were 1800 tickets sold and there are only "adult" and "student" tickets, there must be 1800- x student tickets. The money brought in by x adult tickets is 15x and the money brought in by 1800- x student tickets is 9(1800- x).

 

[babybells96]

I think I get it now. Thank you so much for your help!