If I have cashews for 7.30 a pound an Brazil nuts for 5.40 a pound how much of each is used to make a 28 pound mixture for 6.28 a pound
c + b = 28
so c= 28 - b
7.30 c + 5.40 b = 6.28 * 28 = 175.84
7.30 (28 - b) + 5.40 b = 175.84
204.4 - 7.30 b + 5.40 b = 175.84
204.4 -175.84 = (7.30 -5.40) b
b = 28.6 / 1.9 = 15 pounds of Brazil nuts
etc
To find out how much of each type of nut is needed to make a 28-pound mixture, we can use a system of equations.
Let's assume x represents the number of pounds of cashews and y represents the number of pounds of Brazil nuts.
Given that the cashews cost $7.30 per pound, the cost of cashews in the mixture would be 7.30x dollars. Similarly, the cost of Brazil nuts in the mixture would be 5.40y dollars.
The total cost of the mixture is given as $6.28 per pound, so the total cost of the 28-pound mixture would be 6.28 * 28 = 175.84 dollars.
So, we can set up the following equations:
1. 7.30x + 5.40y = 175.84 (equation 1 - representing the cost of the mixture)
2. x + y = 28 (equation 2 - representing the total weight of the mixture)
Now, we can solve these equations simultaneously to find the values of x and y.
One way to solve this system of equations is by substitution. We can solve equation 2 for x in terms of y:
x = 28 - y
Now, substitute this value of x into equation 1:
7.30(28 - y) + 5.40y = 175.84
Simplify this equation:
204.4 - 7.3y + 5.4y = 175.84
204.4 - 1.9y = 175.84
Rearrange the equation:
-1.9y = 175.84 - 204.4
-1.9y = -28.56
Divide both sides by -1.9:
y = -28.56 / -1.9
y ≈ 15.03
Now, substitute the value of y back into equation 2 to find x:
x + 15.03 = 28
x ≈ 12.97
Therefore, to make a 28-pound mixture priced at $6.28 per pound, you would need approximately 12.97 pounds of cashews and 15.03 pounds of Brazil nuts.