Incorporating Variables

[falconpunch]

At the gospel choir concert, adult tickets are $5.00 and child tickets
are $2.00. The box office indicates that 295 tickets were sold and
they made $1220. How many adult tickets were sold?

I'm sure that you're supposed to incorporate the variables so that
they are equal to both the amount of tickets sold and the money
gained, as well as the problem involving subtraction somewhere. How do
I start, though?

 

[Mrspi]

At the gospel choir concert, adult tickets are $5.00 and child tickets
are $2.00. The box office indicates that 295 tickets were sold and
they made $1220. How many adult tickets were sold?

I'm sure that you're supposed to incorporate the variables so that
they are equal to both the amount of tickets sold and the money
gained, as well as the problem involving subtraction somewhere. How do
I start, though?

An excellent place to start is to NAME THINGS (thanks, TKHunny!).

Let x = number of adult tickets
Let y = number of student tickets

Now, you are told that there are 295 tickets sold in all, so

number of adult tickets plus number of student tickets is 295

x + y = 295

Next, let's look at the amount of money taken in.

If you sell x adult tickets at $5 each, you'll take in 5x dollars. If you sell y student tickets at $2 each, you'll take in 2y dollars. We know that the total amount received was $1220. So,

amount from adult tickets plus amount from student tickets is $1220.

5x + 2y = 1220

Ok...there you go! You have two equations in two variables:

x + y = 295
5x + 2y = 1220

Use your favorite method to solve this system. If you are still having trouble, please repost, showing what you have done to try to solve this system.