Answer:
22.15 pounds of cashews
22.85 pounds of Brazil nuts.
Step-by-step explanation:
Let's call x the number of cashews and y the number of Brazil nuts.
If the mixture should weigh 45 pounds, we can write the following equation:
x + y = 45
On the other hand, it should be sell for $5.64, so we can write the second equation:
6.3x + 5y = 5.64(45)
6.3x + 5y = 253.8
Because 6.3 is the price per pound of the cashews, 5 is the price of the Brazil nuts and 5.64 is the price per pound of the mixture of 45 pounds.
Then, we have the following system of equation:
x + y = 45
6.3x + 5y = 253.8
Solving for y in the first equation, we get:
x + y = 45
x + y - x = 45 - x
y = 45 - x
Now, substitute y = 45 - x on the second equation:
6.3x + 5(45 - x) = 253.8
6.3x + 5(45) - 5(x) = 253.8
6.3x + 225 - 5x = 253.8
Solve for x:
1.3x + 225 = 253.8
1.3x + 225 - 225 = 253.8 - 225
1.3x = 28.8
1.3x/1.3 = 28.8/1.3
x = 22.15
Finally, substitute x = 22.15 and solve for y:
y = 45 - x
y = 45 - 22.15
y = 22.85
Therefore, the answer is:
22.15 pounds of cashews
22.85 pounds of Brazil nuts.