Acharity fair raised $6,000 by selling 500 lottery tickets. there were two types of lottery tickets: a ticket costs $10 each and a b ticket costs $60 each. how many tickets of each type were sold

We have 2 types of tickets, A tickets and B tickets.  The total number of tickets sold was 500, so an equation for this NUMBER of tickets is A + B = 500.  The MONEY equation is something different.  A tickets cost 10, so they are represented by 10A; B tickets cost 60, so they are represented by 60B.  The total dollar sales for A and B are 6000.  Our money equation for the sales is 10A + 60B = 6000.  Solve the first equation for A:  A = 500 - B.  Sub that value for A into the second equation to solve for B:  10(500-B) + 60B = 6000.  Distribute through the parenthesis to get 5000 - 10B + 60B = 6000.  Combine like terms to get 50B = 1000.  B = 20.  There were 20 type B tickets sold.  A = 500 - B, so A = 500 - 20 and A = 480.  There were 480 type A tickets sold.