Questions: Business: Mixing Nuts A nut store normally sells cashews for 9.00 per pound and almonds for 3.50 per pound. But at the end of the month, the almonds had not sold well, so, in order to sell 60 pounds of almonds, the manager decided to mix the 60 pounds of almonds with some cashews and sell the mixture for 7.50 per pound. How many pounds of cashews should be mixed with the almonds to ensure no change in the profit?

Solution Steps

The total cost of 60 pounds of almonds is calculated as follows: \[ \text{Cost of Almonds} = 60 \, \text{pounds} \times 3.50 \, \text{dollars/pound} = 210 \, \text{dollars} \]

Let \( x \) be the number of pounds of cashews to be mixed with the almonds. The total cost of the cashews is given by: \[ \text{Cost of Cashews} = x \, \text{pounds} \times 9.00 \, \text{dollars/pound} \] The total revenue from selling the mixture (60 pounds of almonds and \( x \) pounds of cashews) at $7.50 per pound is: \[ \text{Revenue} = (60 + x) \, \text{pounds} \times 7.50 \, \text{dollars/pound} \] Setting the total cost equal to the total revenue gives us the equation: \[ 210 + 9x = 7.5(60 + x) \]

Expanding the revenue equation: \[ 210 + 9x = 450 + 7.5x \] Rearranging the equation: \[ 9x - 7.5x = 450 - 210 \] This simplifies to: \[ 1.5x = 240 \] Dividing both sides by 1.5: \[ x = \frac{240}{1.5} = 160 \]

Final Answer