Question

The nut shack sells hazelnuts for $7.00 per pound and peanuts nuts for $4.30 per pound. How much of each type should be used to make a 23 pound mixture that sells for $5.47 per pound? Round answers to the nearest pound.

1) pounds of hazelnuts
2) pounds of peanuts nuts

Answer 1

To make a 23 pound mixture that sells for $5.47 per pound with hazelnuts priced at $7.00 per pound and peanuts priced at $4.30 per pound, you will need 8 pounds of hazelnuts and 15 pounds of peanuts.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the number of pounds of hazelnuts 'x' and the number of pounds of peanuts 'y'. Since we want a 23 pound mixture, we can write the equation x + y = 23.

Next, we need to consider the cost per pound of the mixture. The cost of hazelnuts is $7.00 per pound and the cost of peanuts is $4.30 per pound. The cost per pound of the mixture is given as $5.47. We can write the equation 7x + 4.30y = 5.47 * 23.

Solving this system of equations will give us the number of pounds of hazelnuts and peanuts needed to make the 23 pound mixture. Once we have the values of 'x' and 'y', we can round them to the nearest pound to find the pounds of hazelnuts and peanuts needed.

After solving the system of equations, we find that we need approximately 8 pounds of hazelnuts and 15 pounds of peanuts.