Find the # of adult tickets sold

Question

The tickets for a play cost $5.00, and children's tickets cost $2.00.  For one performance, 460 tickets were sold.  Receipts for the performance were $1,880.  Find the number of adult tickets sold.

Answer 1

Let's use some variable to represent key parts of the problem

a = adult tickets

c = children's tickets

 

Translate word problem into algebra expression:

460 tickets were sold -> there were 460 adult and children's tickets -> 460=a+c

 

Receipts for the performance were $1,880 -> receipts for adult tickets ($5 each) and receipts for children tickets ($2 each)equals $1,880 ->  5a+2c=1880

 

By substitution:

  Rewrite 460=a+c by subtracting a from both sides -> 460-a=c

  Substitute for c in 5a+2c=1180

                             5a+2(460-a)=1880

                             5a+920-2a=1880

                             3a+920=1880

                                 -920   -920  

                                 3a = 960

                                   a = 320

 

You can also solve this problem by elimination. 

                            

Answer 2

Michelle, this is a system of equations.  Let's let a = the number of adult tickets and c = the number of children's tickets.

 

Since the number of tickets sold was 460, then we know that a + c = 460. We then need to "solve" this for either a or c.  Let's do a.  Subtracting c from both sides, we get a = 460 - c.

 

Now, let's say we sold 2 adult tickets.  We made $5(2) = $10, right?  Selling "a" tickets, we made $5a.  We also made $2c on children's tickets.  Together, we made $1880, so 5a + 2c = 1880.

 

Now, we can take the "value" we found for a in the first equation and plug it into the 2nd equation for a.

5(460 - c) + 2c = 1880

 

I bet you can solve from here for c.  Then, take that value for c and plug it back into the first equation to find a.  Go for it!