At the Boxer carnival, you can exchange 40 tickets for various assortments of
prizes. Some of those assortments are below. How many tickets does it take
to get a single tacky mirror?
1 goldfish, 2 tacky mirrors, 1 stuffed tiger
5 goldfish, 1 stuffed tiger
2 goldfish, 3 tacky mirrors

g = number of tickets for goldfish

t = number of tickets for tacky mirrors

s = number of tickets for stuffed tiger

1g + 2t + 1s = 40

5g +     + 1s = 40

2g + 3t         = 40

using the second equatin we can find a value for s

1s = 40 -5g

now substitute in the first equation to get rid of s

1g + 2t + (40-5g) = 40

-4g + 2t         = 0

now use this new equation with equation 3 and solve for one of the values

-4g + 2t = 0

2g + 3t  = 40

multipy the second equation by 2 and then combine

-4g + 2t = 0

 4g + 6t = 80

8t = 80

t = 10  (so it takes 10 tickets to get a takcy mirror)

2g + 3(10) = 40

2g = 10

g = 5  (five tickets to get a goldfish)

s = 40 -5(5)

s = 15  (fifteen tickets for a stuffed tiger)

1(5) + 2(10) + 1(15) (substitute back in the first equation)

5 + 20 + 15

40                    it works!