Question

1. If 2 kilo potato and 3 kilo onion costs 14 while 5 kilo potato and 3 kilo onion costs 26, find the price of potato and kilo cost per kilo. (use: Gauss Jordan Elimination Method)​

Answer 1

To solve the problem using the Gauss Jordan Elimination method, we first need to set up a system of linear equations based on the given information.

Let x be the price of 1 kilo of potato and y be the price of 1 kilo of onion.

From the first statement, we know that:

2x + 3y = 14

From the second statement, we know that:

5x + 3y = 26

We can write this system of linear equations in matrix form as:

[2 3 | 14]

[5 3 | 26]

To solve for x and y, we can use Gauss Jordan Elimination to transform this matrix into row echelon form

[1 0 | 4]

[0 1 | 2]

This tells us that x = 4 and y = 2. Therefore, the price of potato is 4 per kilo and the cost per kilo is 2 per kilo.

So, 2 kilos of potato cost 8 and 3 kilos of onion cost 6, which adds up to 14. And 5 kilos of potato cost 20 and 3 kilos of onion cost 6, which adds up to 26, confirming that our solution is correct

Answer 2

Step-by-step explanation:

ELet's use a system of equations to represent the given information:

2p + 3o = 14

5p + 3o = 26

where p is the price of 1 kilo of potato and o is the price of 1 kilo of onion.

We can solve this system of equations using Gauss Jordan elimination:

[ 2 3 | 14 ]

[ 5 3 | 26 ]

Divide Row 1 by 2:

[ 1 3/2 | 7 ]

Multiply Row 1 by -5 and add to Row 2:

[ 1 3/2 | 7 ]

[ 0 -9/2 | -3 ]

Divide Row 2 by -9/2:

[ 1 3/2 | 7 ]

[ 0 1 | 6/9 ]

Subtract 3/2 times Row 2 from Row 1:

[ 1 0 | 2 ]

[ 0 1 | 2/3 ]

Therefore, the solution is p = 2 and o = 2/3, which means the price of 1 kilo of potato is 2 and the price of 1 kilo of onion is 2/3.

To check the solution, we can substitute p = 2 and o = 2/3 into the original equations:

2(2) + 3(2/3) = 4 + 2 = 14 (checks out)

5(2) + 3(2/3) = 10 + 2 = 26 (checks out)

Therefore, the solution is correct.