2) Edwin A bought a total of 15 student and non-student tickets worth $223.50. The student tickets cost $12.50 each and the non-student tickets cost $18.50 each. How many of each ticket did he buy?

I imagine you are in the section in math that teaches about systems! We need a system here to solve this problem...meaning we have 2 unknowns and we need to write 2 equations to solve for them. The first equation will involve the NUMBER of tickets sold, while the second equation will involve the COST of the tickets. These are 2 very different things, and we have what we need to write each equation. First the number of tickets equation:

We know that the number of student tickets (s) and the number of non-student tickets (n) totaled 15 tickets. That means the numbers equation is

s + n = 15

Now onto the money. Since s is student tickets, and each student ticket cost 12.50, the expression for that is 12.5s; since n is non-student tickets and each non-student ticket cost 18.50, the expression for that is 18.5n. That is the money expression for each type of ticket, and we know that the sales of these tickets totaled 223.50; therefore, the money equation is

12.5s + 18.5n = 223.5 (notice I dropped off the 0's since we don't need them).

Go back to the first equation and solve it for either s or n. I solve is for s:

If s + n = 15, then

s = 15 - n. Sub that into the second equation in place of s now:

12.5(15 - n) + 18.5n = 223.5 and simplify a bit by distributing to get

187.5 - 12.5n + 18.5n = 223.5 and combine like terms to get

6n = 36 so

n = 6. That means that there were 6 non-student tickets sold and

s + 6 = 15 student tickets sold:

s = 15 - 6 so

s = 9