walnuts that sell for $3 a pound and macadamia nuts that sell for $4 per pound are mixed to create 50 pounds of mixture that sells for $4 per pound. HOw many pounds of each type of nut are needed?
They could be all macademia nuts.
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To solve this problem, we can use a system of equations. Let's assume x pounds of walnuts and y pounds of macadamia nuts are needed to create the 50-pound mixture.
1. The first equation represents the total weight of the mixture:
x + y = 50
2. The second equation represents the total cost of the mixture:
3x + 4y = 4 * 50
Now we can solve this system of equations to find the values of x and y.
Step 1: Solve equation 1 for x:
x = 50 - y
Step 2: Substitute the value of x in equation 2:
3(50 - y) + 4y = 200
150 - 3y + 4y = 200
150 + y = 200
y = 200 - 150
y = 50
Step 3: Substitute the value of y back into equation 1 to find x:
x + 50 = 50
x = 0
Therefore, to create a 50-pound mixture that sells for $4 per pound, you would need 0 pounds of walnuts and 50 pounds of macadamia nuts.