Algebra two 3 variable matrix question. Find three variables and three equations for the matrix from the word problem.

Question

1. An Oil Company in the US does business with three suppliers in Toronto, Montreal, and Vancouver. One month the company ordered a total of 100 gallons from these suppliers. The delivery costs were $80, $50, and $65 per gallon for the orders from Toronto, Montreal, and Vancouver, respectfully, with total delivery costs of $5,990. The company ordered the same amount from Toronto and Vancouver. How many gallons of oil were ordered from each supplier?

Answer 1

The three equations are:

x + y + z = 100

80x + 50y + 65z = 5990

x - z = 0

Putting into matrix form

[ 1 1 1 100]

[80 50 65 5990]

[ 1 0 -1 0]

Doing several Row operations to get the matrix in row echelon form

[80 50 65 5990]

[0 10 29 1198]

[0 0 1 22]

So z = 22 = x x = z from description

y = 100 -√22 - 22 = 56

Toronto and Vancouver each supplied 22 gallons

Montreal supplied 56 gallons

Checking delivery cost: 80(22) + 50(56) + 65(22) = 1760 + 2800 + 1430 = $5990 √

Answer 2

Algebra two 3 variable matrix question. Find three variables and three equations for the matrix from the word problem.

============WORD PROBLEMS ARE FUN===============

============READ THEM 2 OR 3 TIMES TO GET THE FACTS CORRECT=====

1. An Oil Company in the US does business with three suppliers in Toronto, Montreal, and Vancouver. One month the company ordered a total of 100 gallons from these suppliers. The delivery costs were $80, $50, and $65 per gallon for the orders from Toronto, Montreal, and Vancouver, respectfully, with total delivery costs of $5,990. The company ordered the same amount from Toronto and Vancouver. How many gallons of oil were ordered from each supplier?

In word problems there are always unknown you are trying to figure out. So you substitute variables for unknowns in order to WRITE the equations......so......

It is unknown "The Amount of fuel in gallons" ordered from each supplier....so.....we let....

T = amount of fuel ordered from Toronto

V = amount of fuel ordered from Vancouver

M = amount of fuel ordered from Montreal

=======Now from the facts of the problems we have our THREE equations and THREE unknowns=====

T + V + M = 100.........................Number of Gallons

T80 + V50 + M65 = 5990............Total Delivery Costs

T = V ..........................................same amount from Vancouver and Toronto