Question

HELP PLEASE!

Flex N Furious Luxury Car dealership owner purchases eight sedans and six sport utility vehicles for his Capital Heights and District Heights location. The Capital Heights locations receives five of the sedans and two of the SUV's for a total cost of one hundred and eighty-nine thousand dollars. The District Heights locations receives three of the sedans and four of the SUV's for a total cost of two hundred and three thousand dollars. What is the cost for each type of sedan and each type of SUV? Write and solve your answer by creating a system of equations. Provide evidence of your answer and write your answer in a complete sentence.

Answer 1

The cost of each sedan is twenty five thousand dollars while the cost of each SUV is thirty two thousand dollars

Explanation:

The given parameters are;

The number of sedans the Flex N Furious Luxury Car dealership owner purchases = 8 sedans

The number of sport utility vehicles the Flex N Furious Luxury Car dealership owner purchases = 6 sport utility vehicles

The number of sedans the Capital Height locations receive = 5 sedans

The number of sport utility vehicles the Capital Height locations receive = 2 sport utility vehicles

The total cost of the cars received by the Capital Height locations = $189,000

The number of sedans the District Height locations receive = 3 sedans

The number of sport utility vehicles the District Height locations receive = 4 sport utility vehicles

The total cost of the cars received by the District Height locations = $203,000

To answer the question, we proceed as follows;

Let, x represent the cost of each sedan and let y represent the cost of each sport utility vehicle

From the question, we have;

For the Capital Height locations

5·x + 2·y = 189,000...(1)

For the District Height locations

3·x + 4·y = 203,000...(2)

Making y the subject of both equations gives;

For equation (1) 5·x + 2·y = 189,000

y = (189,000 - 5·x)/2 = 94,500 - 2.5·x

y = 94,500 - 2.5·x

For equation (2) 3·x + 4·y = 203,000

y = (203,000 - 3·x)/4 = 50,750 - 0.75·x

y = 50,750 - 0.75·x

The solution is given by the point where both equations are equal, therefore, we have;

The solution for the x-values, is where 94,500 - 2.5·x = 50,750 - 0.75·x

Which gives;

94,500 - 50,750 = 2.5·x - 0.75·x

43,750 = 1.75·x

x = 43,750/1.75 = 25,000

x = 25,000

The cost of each sedan = x = $25,000

The y-value at the common x-value is the solution for the common y-values given as follows;

From y = 50,750 - 0.75·x, substituting, x = 25,000, gives;

y = 50,750 - 0.75 × 25,000 = 32,000

y = 32,000

The cost of each sport utility vehicle = y = $32,000

The evidence of the above answers are;

The total cost of the cars received by the Capital Height locations, C, is given as follows;

C = Cost of 5 sedans + Cost of 2 Sports utility vehicles

5 × 25,000 + 2 × 32,000 = 189,000

The total cost of the cars received by the Capital Height locations is $189,000 as given in the question

The total cost of the cars received by the District Height locations, D, is given as follows;

D = Cost of 3 sedans + Cost of 4 Sports utility vehicles

3 × 25,000 + 4 × 32,000 = 203,000

The total cost of the cars received by the District Height locations is $203,000 as given in the question

Therefore, we have the cost of each sedan is twenty five thousand dollars while the cost of each SUV is thirty two thousand dollars.