Linear Systems: 3 Variables

Question

Last year, at Haven's Pond Car Dealership, for a particular model of BMW, Jeep, and Toyota, one could purchase all three cars for a total of $140,000. This year, due to inflation, the same cars would cost $151,830. The cost of the BMW increased by 8%, the Jeep by 6%, and the Toyota by 10%. If the price of last year's Jeep was $6,000 less than the price of last year's BMW, what was the price of each of the three cars last year? (Round your answers to the nearest integer.)

Answer 1

Let B = price of the BMW last year

J = last year's Jeep price

T = last year's Toyota price.

B + J + T = 140,000

Because of inflation, they cost more now:

(1.08)B + (1.06)J + (1.1)T = 151,830

And the third equation comes from the Jeep being less expensive.

B - J = 6000

Those are the three equations. Solve them for B, J and T and you have the answer.