Question

The cost of 4kg potato, 3kg wheat and 2k rice is Rs. 150. The cost of 1 kg potato
2 kg wheat and 3 kg riceis Rs. 125. The cost of 6 kg potato, 2 kg wheat and 3 kg
rice is Rs. 175. Find the cost of each item per kg using Cramer's rule.​

Answer 1

Answer:

78-68

Step-by-step explanation:

you can consider it as mathematics in measurement by kg and g

Answer 2

Therefore the cost of potato is Rs. 5 per kg,the cost of wheat is Rs.20 per kg and the cost of rice is Rs. 25 per kg.

Step-by-step explanation:

Let,the cost price of 1 kg of potato be x,1 kg of wheat be y and 1kg of rice be z.

Given that, the cost of 4 kg potato, 3 kg wheat and 2 kg rice is Rs.150.

Then  the cost of 4 kg potato is=Rs. 4 x

the cost of 3 kg wheat is=Rs. 3 y

the cost of 2 kg rice is=Rs. 2 z

Therefore ,

4x+3y+2z= 150.........(1)

Given that, the cost of 1 kg potato, 2 kg wheat and 3 kg rice is Rs.125.

Then  the cost of 4 kg potato is=Rs.x

the cost of 3 kg wheat is=Rs.2y

the cost of 2 kg rice is=Rs. 3 z

Therefore, x+2y+3z= 125...........(2)

Given that, the cost of 6 kg potato, 2 kg wheat and 3 kg rice is Rs.175.

Then  the cost of 6 kg potato is=Rs. 6x

the cost of 2 kg wheat is=Rs. 2y

the cost of 3 kg rice is=Rs. 3z

Therefore , 6x+2y+3z=175............(1)

Cramer's rule:

a₁x+b₁y+c₁z=d₁

a₂x+b₂y+c₂z=d₂

a₃x+b₃y+c₃z=d₃

$D=\left|\begin{array}{ccc}a_1&b_1&c_1\\a_2&b_2&c_2\\a_3&b_3&c_3\end{array}\right|$    

$D_x=\left|\begin{array}{ccc}d_1&b_1&c_1\\d_2&b_2&c_2\\d_3&b_3&c_3\end{array}\right|$

$D_y=\left|\begin{array}{ccc}a_1&d_1&c_1\\a_2&d_2&c_2\\a_3&d_3&c_3\end{array}\right|$

$D_z=\left|\begin{array}{ccc}a_1&b_1&d_1\\a_2&b_2&d_2\\a_3&b_3&d_3\end{array}\right|$

Then $x=\frac{D_x}{D}$ ,  $y=\frac{D_y}{D}$ and $z=\frac{D_z}{D}$

Here a₁=4,b₁=3,c₁=2,a₂=1,b₂=2,c₂=3,a₃=6,b₃=2,c₃=3,d₁=150,d₂=125,d₃=175

$D=\left|\begin{array}{ccc}4&3&2\\1&2&3\\6&2&3\end{array}\right|$     =25

$D_x=\left|\begin{array}{ccc}150&3&2\\125&2&3\\175&2&3\end{array}\right|$ =125

$D_y=\left|\begin{array}{ccc}4&150&2\\1&125&3\\6&175&3\end{array}\right|$=500

$D_z=\left|\begin{array}{ccc}4&3&150\\1&2&125\\6&2&175\end{array}\right|$=625

According to Cramer's rule

$x=\frac{D_x}{D}$$=\frac{125}{25} =5$

$y=\frac{D_y}{D}=\frac{500}{25}=20$

$z=\frac{D_z}{D}=\frac{625}{25}= 25$

Therefore the cost of potato is Rs. 5 per kg,the cost of wheat is Rs.20 per kg and the cost of rice is Rs. 25 per kg.