A nut wholesalersells a mix of peanuts and cashews. He charges $2.80 per pound for peanuts and $5.30 per pound for cashews. If the mix of peanuts and cashwes is to sellfor $3.30 pre pount, how many pound each of the peanuts and cashews should be used to marke 100 pounds of mix nuts?
If there are x lbs of peanuts, then there are (100-x) lbs of cashews. So work with the value of the mixture and its parts:
2.80x + 5.30(100-x) = 3.30(100)
To solve this problem, we can use a system of equations. Let's assume that x represents the number of pounds of peanuts and y represents the number of pounds of cashews.
According to the problem, we know that the mix of peanuts and cashews should sell for $3.30 per pound. This can be expressed as the following equation:
2.80x + 5.30y = 3.30(100)
Now, we have another equation based on the total weight of the mix nuts, which is given as 100 pounds:
x + y = 100
We can now solve this system of equations to find the values of x and y.
First, let's multiply the second equation by 2.80 to eliminate x:
2.80(x + y) = 2.80(100)
2.80x + 2.80y = 280
Now, we have the following system of equations:
2.80x + 5.30y = 3.30(100)
2.80x + 2.80y = 280
By subtracting the second equation from the first equation, we can eliminate x:
(2.80x + 5.30y) - (2.80x + 2.80y) = (3.30(100) - 280)
2.50y = 50
Now, we can solve for y:
y = 50 / 2.50
y = 20
Now, substitute the value of y back into the second equation to find x:
x + 20 = 100
x = 100 - 20
x = 80
Therefore, to make 100 pounds of mix nuts, you should use 80 pounds of peanuts and 20 pounds of cashews.