The management of Hartman Rent-A-Car has allocated 2.25 million to buy a fleet o

Question

The management of Hartman Rent-A-Car has allocated 2.25 million to buy a fleet of new of automobiles consisting of compact, intermediate-size and full sized cars. Compact cars cost $18,000 each, intermediate cost $27,000 and a full size is $36,000 each. If Hartman purchases twice as many compacts as intermediate-size cars and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. (assume the entire budget will be used) USE THE GAUSS-JORDAN METHOD OF ELIMNATION

Explanation / Answer

Let compact = C, intermediate = I, and full size = F $2.25 million is available, so 18000 C + 27000 I + 36000 F = 2250000 Twice as many compacts as intermediate size cars are built, so C = 2I, 100 cars are purchased, so C + I + F = 100 We can substitute C = 2I into the last equation, C + I + F = 100, so 2I + I + F = 100, or 3I + F = 100, or F = 100 - 3I Then, you can substitute both F and C into 18000 C + 27000 I + 36000 F = 2250000 18000(2I) + 27000 I + 36000(100 - 3I) = 2250000 3600000 - 45000 I = 2250000 1350000 = 45000 I I = 30 C = 2I = 60 F = 100 - 3I = 10 As a check, plugging into the 3 equations, 18000 C + 27000 I + 36000 F = 18000*60 + 27000*30 + 36000*10 = 2250000 C = 60, and I = 30, and 60 = 2 * 30 C + I + F = 60 + 30 + 10 = 100

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