You are on the right track, but you made a small mistake in interpreting the given data. Let's correct it and find the matrices.
Let x be the number of days (4 days) and y be the number of kilometers driven (560 km).
The charges of each company can be represented as follows:
Company A: 660x
Company B: 48y
Company C: 300x + 150y
The 3x1 matrix for the charges would look like this:
| 660x |
C = | 48y |
| 300x+150y |
Now, we need to find the matrix that when multiplied by C gives the charges of the three companies. That matrix should have two elements: x (number of days) and y (number of kilometers driven). So, the 2x1 matrix would look like this:
| 4 |
D = |560 |
Now let's find the product of these two matrices to find the charges from each company:
E = CD
| 660*4 | | 4 | | 2640 |
E = | 48*560 | * |560 | = | 26880 |
| 300*4+150*560 | | 97800 |
The matrix E now contains the charges for each company:
Company A: $2640
Company B: $26880
Company C: $97800
To save cost, John should hire the car from Company A.
The charges for hiring a car from three different companies, based on the number of days for which a car is hired and/or number of kilometres for which the car is driven are as follows:
Company A charges $660 per day
Company B charges 48 cents on per kilometre driven
Company C charges $300 per day and $150 on per kilometre driven
John needs to hire a car for 4 days to drive 560 kilometres
(i) Write down two matrices only such that the elements of their product under matrix multiplication give the charge of hiring a car from three different companies
(ii) Find this product. Hence, state the company that John should hire the car in order to save cost.
My answer:
The number of days - x; number of kilometres driven - y
Thus, (660x) =
(48y) =
(300x +150y)
This above is supposed to be a 3x1 matrix
I would equate all of these matrices to the 2x1 matrix (4x) (5y)
Please tell me if I'm on the right track. Thank you.
1 answer