Question

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?"

Option 1: 10 pounds
Option 2: 20 pounds
Option 3: 30 pounds
Option 4: 40 pounds

Answer 1

To ensure no change in profit, 30 pounds of cashews should be mixed with the almonds.

Step-by-step explanation:

To find the number of pounds of cashews that should be mixed with the almonds, we need to consider the price difference and the desired selling price of the mixture. Let's assume x pounds of cashews are mixed with the almonds.

The cost of almonds alone would be 60 pounds * $3.50/pound = $210.

The cost of the mixture at $7.50/pound would be (60+x) pounds * $7.50/pound.

In order to ensure no change in profit, the total cost of the mixture should be equal to the cost of the almonds. So, we can set up the equation: $210 = (60+x) * $7.50.

By solving the equation, we find that x = 30 pounds. Therefore, 30 pounds of cashews should be mixed with the almonds to ensure no change in profit.