SOLUTION: How do I solve the following problem? I need 100 pounds of mixed nuts (peanuts and cashews). The peanuts will cost me $3.00 per pound and the cashews will cost me $4.00 per pound.

Question 295960: How do I solve the following problem? I need 100 pounds of mixed nuts (peanuts and cashews). The peanuts will cost me $3.00 per pound and the cashews will cost me $4.00 per pound. How do I find out how many pounds of each kind of nut I should buy? How can I set up a system of equations to find the correct solution?
Found 2 solutions by richwmiller, Theo:
Answer by richwmiller(17219) (Show Source): You can put this solution on YOUR website!
I think you might be missing some info but let's continue.
p+c=100
3*p+4*c=100x
You are missing the final cost of the mix.
We have two equations and three unknowns
We can get it down to one equation and 2 unknowns. But we need at least one equation for each unknown.
3p+4(100-p)=100x
We do know that p is less than 100
and that x is between 3 and 4
x=4-p/100
if p=60 then the cost of the mix will be $3.40
if p=40 then the mix will cost $3.60
The more peanuts the lower the cost
The more cashews the higher the cost

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
p = pounds of peanuts
c = pounds of cashews
3p = cost for peanuts
4c = cost for cashews

Your equations are:

p + c = 100 (you need 100 pounds of mixed nuts)
3p + 4c = x (it will cost you x number of dollars)

You need to find a value for x which you will be able to spend.

x will have to be greater than or equal to $300 (all peanuts).
x will have to be less than or equal to $400 (all cashews).

Assume x is $375.00

This means that you can spend $375.00 on mixed nuts.

Your formulas become:

p + c = 100
3p + 4c = 375

You would then solve these 2 equations simultaneously to find out how many pounds of peanuts and cashews you can buy.

Multiply the first equation by 3 to get:

3p + 3c = 300
3p + 4c = 375

Subtract the first equation from the second equation to get:

c = 75

Since p + c = 100, this means that p = 25.

Total cost would be 25*3 + 75*4 = 75 + 300 = $375.00.

With $375.00, you can buy 25 pounds of peanuts and 75 pounds of cashews.

If you only had $325 to spend, then your equations would have been:

p + c = 100
3p + 4c = 325

Multiply first equation by 3 to get:

3p + 3c = 300
3p + 4c = 325

Subtract first equation from second equation to get:

c = 25

If c = 25, then p = 75, because p + c = 100

Total cost would be 75*3 + 25*4 = 225 + 100 = $325.00

If you had $325.00 to spend, you could buy 75 pounds of peanuts and 25 pounds of cashews.

So:

With $375 to spend, you could buy 25 pounds of peanuts and 75 pounds of cashews.
With $325 to spend, you could buy 75 pounds of peanuts and 25 pounds of cashews.

The amount of money you had to spend between $300 and $400 determines how many pounds of peanuts you can buy versus how many pounds of cashews you can buy in order to get 100 pounds of mixed nuts.

If you had less than $300 to spend, you would not be able to buy 100 pounds, no matter what mix you chose.

If you had more than $400 to spend, you would have money left over, no matter what mix you chose.

You only needed between $300 and $400 in order for the pounds to be equal to 100 pounds and no money to be left over.
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