Question

The owner of a shop wants to mix cashews and pecans to make 8 kg of mixed nuts worth $7.25 per kg. If the price of cashews is $8.00 per kg and the price of pecans is $7.00 per kg, how many kilograms of each should he take?

Answer 1

Answer:

6 kg pecans,

2 kg cashews.

Step-by-step explanation:

Let x be the weight of cashews and y be the weight of pecans in kg.

We have been given that the owner of a shop wants to mix cashews and pecans to make 8 kg of mixed nuts. We can represent this information in an equation as:

$x+y=8...(1)$

We are also told that the mixed nuts worth $7.25 per kg, so the price of 8 kg of mixed nuts will be $\ 7.25\times 8=\ 58$.

Since the price of cashews is $8.00 per kg and the price of pecans is $7.00 per kg, so we can represent this information in an equation as:

$8x+7y=58...(2)$  

Now we will use substitution method to solve system of equations.

From equation (1) we will get,

$x=8-y$

Substituting this value in equation (2) we will get,

$8(8-y)+7y=58$

$64-8y+7y=58$

$64-y=58$

$64-64-y=58-64$

$-y=-6$

$y=6$

Therefore, the owner should take 6 kg of pecans.

Upon substituting $y=6$ in equation (1) we will get,

$x+6=8$

$x+6-6=8-6$

$x=2$

Therefore, the owner should take 2 kg of cashews.

Answer 2

Answer:

Weight of Cashew = 2Kg  

Weight of Pecan = 6Kg

Step-by-step explanation: