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

Weight of Cashew = 2Kg

Weight of Pecan = 6Kg

Explanation:

Answer 2

6 kg pecans,

2 kg cashews.

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* 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.