SOLUTION: SOLVE USING DETERMINANTS and CRAMER'S RULE Three kilos of homegrown tobacco and 8 kilos of imported tobacco cost $39.70 ,and 5 kilos of homegrown tobacco and 6 kilos of imported

Click here to see ALL problems on Linear Equations And Systems Word Problems

Question 208211: SOLVE USING DETERMINANTS and CRAMER'S RULE
Three kilos of homegrown tobacco and 8 kilos of imported tobacco cost $39.70 ,and 5 kilos of homegrown tobacco and 6 kilos of imported tobacco cost $47.10. What is the cost per kilo for both kinds of tobacco?
Answer by pjalgeb(9) (Show Source):
You can put this solution on YOUR website!
REQUIRED: Find y(price of homegrown tobacco) and x(price of imported tobacco)

SOLUTION:

Amount HGT Amount of IMPT IMPT Price HGT Price Total Price
(kilos) (kilos) ($ per kilo) ($ per kilo) ($)
______________________________________________________________________________
First Order | 3 : 8 : x : y : 3x+8y = 39.7 |
Second Order | 5 : 6 : x : y : 5x+6y = 47.1 |
______________________________________________________________________________

The following Equations can be derived from the total price column:
--> Equation 1 and
--> Equation 2

Now we have two equations with two unknowns:
3x+8y = 39.7 --> Equation 1
5x+6y = 47.1 --> Equation 2

The augmented 2x2 matrix for the above system of equations is:
| 3 8 | 39.7 |
| 5 6 | 47.1 |

Using Cramer's Rule:

First we solve for D, Dx and Dy:
D = | 3 8 | = 3(6) - 8(5) = 18 - 40 = - 22
| 5 6 |
since D is not 0 then we can proceed:

Dx = | 39.7 8 | = 39.7(6) -8(47.1) = 238.2 - 376.8 = -138.6
| 47.1 6 |

Dy = | 3 39.7 | = 3(47.1) - 5(39.7) = 141.3 - 198.5 = -57.2
| 5 47.1 |

Now we can solve for x and y:

ANSWER:
Homegrown tobacco costs $2.60 per kilo while the imported ones costs $6.30 per kilo.