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 @@MATH_TOKEN_1@@.
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.
