Walnuts sell for $10 per pound and pecans for $18 per pound. How much of each type of nut would produce 40 pounds of a mix that sells for $15 per pound?
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And I am very appreciative of the help I've gotten so far. I sincerely am. I am unsure how to set up this problem?
Try different methods until you find a reasonable answer.
I would love to try that, but I have no idea where to begin. I don't have class until tomorrow night, so I cannot ask my instructor. I am not trying to be selfish with the help I've received from this site. I am grateful and I genuinely need help.
The best way to learn is to try to do these math problems. We all learn by trial and error and failing sometimes.
You know that you'll need more than half the mixture must be walnuts. There will probably be around 25 or so pounds of walnuts.
Also -- check out the Related Questions below. They should give you some clues about how to approach this problem.
Let walnut w and pecan p
p = 40-w
10w + 18(40-w) = 40(15)
10w + 720 -18w = 600
-8w + 720 = 600
Solve for w
Any chance you gals would like to go to class with me tomorrow evening? It's 6:00-9:45 pm eastern time in Richmond, IN?
Thank you very much for the assistance, I really do appreciate it more than you know.
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You're very welcome.
To solve this problem, we can use a system of equations. Let's assume x represents the number of pounds of walnuts and y represents the number of pounds of pecans.
From the given information, we know that the total weight of the nut mix is 40 pounds, so we can write the equation:
x + y = 40
We also know that the total cost of the mix is obtained by multiplying the cost per pound of each type of nut with their respective weights and adding them together. This can be expressed as:
10x + 18y = 15(40)
Simplifying the equation, we have:
10x + 18y = 600
Now, we have two equations:
x + y = 40
10x + 18y = 600
There are multiple ways to solve this system of equations, such as substitution or elimination. Let's use the elimination method.
First, multiply the first equation by 10 to make the coefficients of x in both equations the same. We get:
10(x + y) = 10(40)
10x + 10y = 400
Now we can subtract this equation from the second equation to eliminate x:
(10x + 18y) - (10x + 10y) = 600 - 400
8y = 200
Divide both sides of the equation by 8:
y = 25
Now, substitute the value of y back into the first equation and solve for x:
x + 25 = 40
x = 40 - 25
x = 15
Therefore, we need 15 pounds of walnuts ($10 per pound) and 25 pounds of pecans ($18 per pound) to produce 40 pounds of the nut mix that sells for $15 per pound.