Question

Nut Mixture) Ten pounds of mixed nuts sells for $6.87 per pound. The mixture is obtained from two kinds of nuts, peanuts priced at $5.70 per pound and cashews at $8.70 per pound. How many pounds of each variety of nut are used in the mixture? ​

Answer 1

To find the number of pounds of each variety of nut used in the mixture, we can set up a system of equations using their costs per pound. Using the method of elimination, we can solve the system to find that there are 6.1 pounds of peanuts and 3.9 pounds of cashews in the mixture.

Step-by-step explanation:

Let's assume the number of pounds of peanuts in the mixture is x and the number of pounds of cashews is y.

According to the given information, the cost of 1 pound of peanuts is $5.70 and the cost of 1 pound of cashews is $8.70.

So we can set up the following system of equations to represent the given information:

x + y = 10 (since the total weight of the mixture is 10 pounds)

5.70x + 8.70y = 6.87(10) (since the total cost of the mixture is $6.87 per pound)

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

1. Multiply the first equation by 5.70 to eliminate x: 5.70x + 5.70y = 57
2. Subtract the second equation from the first: 5.70x + 8.70y - 5.70x - 8.70y = 57 - 6.87(10)
3. -3y = 57 - 68.7
4. -3y = -11.7
5. y = -11.7/-3
6. y = 3.9
7. Substitute the value of y into the first equation to find x: x + 3.9 = 10
8. x = 10 - 3.9
9. x = 6.1

Therefore, there are 6.1 pounds of peanuts and 3.9 pounds of cashews in the mixture.