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)](https://tex.z-dn.net/?f=x%2By%3D8...%281%29)
We are also told that the mixed nuts worth $7.25 per kg, so the price of 8 kg of mixed nuts will be
.
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:
Now we will use substitution method to solve system of equations.
From equation (1) we will get,
![x=8-y](https://tex.z-dn.net/?f=x%3D8-y)
Substituting this value in equation (2) we will get,
![8(8-y)+7y=58](https://tex.z-dn.net/?f=8%288-y%29%2B7y%3D58)
![64-8y+7y=58](https://tex.z-dn.net/?f=64-8y%2B7y%3D58)
![64-y=58](https://tex.z-dn.net/?f=64-y%3D58)
![64-64-y=58-64](https://tex.z-dn.net/?f=64-64-y%3D58-64)
![-y=-6](https://tex.z-dn.net/?f=-y%3D-6)
![y=6](https://tex.z-dn.net/?f=y%3D6)
Therefore, the owner should take 6 kg of pecans.
Upon substituting
in equation (1) we will get,
![x+6=8](https://tex.z-dn.net/?f=x%2B6%3D8)
![x+6-6=8-6](https://tex.z-dn.net/?f=x%2B6-6%3D8-6)
![x=2](https://tex.z-dn.net/?f=x%3D2)
Therefore, the owner should take 2 kg of cashews.