A car dealership sells Corvettes and Mustangs. A Corvette sells for $65,000 and a Mustang sells for $40,000. The inventory of both cars is worth $1,260,000.

1. Show how this equation is written.

2. Use the elimination method to see how many Mustangs and how many Corvettes are in the inventory.

1--65,000C + 40,000M = 1,260,000

2--Simplifying, 13C + 8M = 252

3--Dividing through by the smallest coefficient, yields

...1C + 5C/8 + 1M = 31 + 4/8

4--Rearranging, (5C - 4)/8 = 31 - C - M

5--(5C - 4)/8 must be an integer k as does (25C - 20)/8

6--Dividing through by 8 yields C + C/8 - 2 - 4/8

7--(C - 4)/8 must be an integer k making C = 8k + 4

8--Substituting back into (2) yields M = 25 - 13k

9--k.....0.....1.....2

...C.....4....12....20

...M....25....12...-1

Therefore, there are 2 possible inventories of 4 Corvettes and 25 Mustangs or 12 of each.