Question

Carter sells cashews for$3.00 dollars a pound, hazelnuts for $2.50 a pond,and peanuts for$1.75 a pound. How many pounds of cashew and hazelnuts should be mixed with 50lbs of peanuts to obtain a mixture of 100lbs that will sell for$2.30 a pound so that the profit or loss is unchanged ?

Answer 1

Here's the equation you need:

3.00x + 2.50x + 1.75(50) = 2.30(2x + 100)

Take it from here.

Answer 2

35 pounds of cashews and 15 pounds of hazelnuts.

Explanation:

Let x pounds of cashew and y pounds hazelnuts is should be mixed with 50lbs of peanuts to obtain a mixture of 100 pounds,

That is,

x + y + 50 = 100

x + y = 50 -----(1),

Also, cashews for $3.00 dollars a pound, hazelnuts for $2.50 a pond,and peanuts for $1.75 a pound.

Thus, the total cost = 3x + 2.50y + 1.75 × 50

= 3x + 2.50y + 87.5,

Since, the cost of the resultant mixture is $ 2.30 per pounds,

So, the total cost = 2.30 × 100 = $ 230

⇒ 3x + 2.50y + 87.5 = 230

⇒ 3x + 2.50y = 142.5 ----(2),

Equation (2) - 3 × equation (1),

-0.50y = 142.5 - 150 = -7.5 ⇒ y = 15,

From equation (1),

x + 15 = 50 ⇒ x = 35

Hence, 35 pounds of cashews and 15 pounds of hazelnuts should be mixed.