Question 184241: I believe the answers are 60, 30, 10 but can't figure out the formula to get there. Thanks! The management of Bozo Rent-A-Car has allocated $1.5 million to buy a fleet of new automobiles consisting of compact, intermediate-size and full-size cars. Compacts cost $12,000 each, intermediates cost $18,000 and full-size cost $24,000 each. If they purchase twice as many compacts as intermediate and the total number of cars to be purchased is 100, determine how many cars of each type will be purchased. The entire budget must be spent.
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
First thing, your answers are correct.
Second thing, we are going to express the dollar amounts in 1000s, so Compacts cost 12, Intermediates cost 18, and Full-size cost 24, and the total amount spent is 1500.
Let x be the number of Intermediates and
Let y be the number of Full-Size and then
2x is the number of Compacts.
We know that:
And, since there are 2x Compacts each costing 12, the cost of the Compacts is 24x. Likewise the cost of the Intermediates is 18x and the cost of the Full-Size is 24y. Finally, the sum of the costs is 1500, so:
Multiply the first equation by -14:
Add this new equation, term-by-term, to the second equation:
Hence, 10 Full-Size cars. Substitute this value into the original first equation:
Hence, 30 Intermediates and 60 Compacts.
John
Answer by josmiceli(19441)  (Show Source):
|
|
|
