twp equations

Question

Tickets to the Taste of Wine Weekend cost $160 on the night of the reception and $140 if purchased in advance.  If 150 tickets were sold for a total of $21,800 how many of the tickets were sold in advance?

Answer 1

Here we only have enough info for one equation, so we can't have two variables, but we have two prices. So we can't have A = advance tickets and T = tickets sold on the night of the show. What to do?

 

Think of it this way. If we let A = the number of advance sale tickets, then 150 - A = the number of tickets sold on the night of the reception. We can get rid of the second variable (T) by representing it in terms of the first, using the fact we know about the total number of tickets. So, here are our variable definitions:

 

A = advance tickets

150 - A = night-of-show tickets

 

You know the price of each type of ticket, and the total revenue. So, you multiply the price times each number of tickets and add the results together to get the total, as follows:

 

140A + 160(150 - A) = 21,800 -->Use distribution next!

140A + 24000 - 160A = 21,800

-20A = -2200  -->Don't worry about the negatives, they'll go away when you divide through by -20

 

A = 110 <-- This is your advance number

 

150-110 = 40 <-- This is your night-of-show number