# Solve a Written Equation Using the Elimination Method

#### Monkeyboy869

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. #### TchrWill ##### Full Member 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.