SOLUTION: a merchant mix peanuts that sells for $3/pound and cashews that sells for $6/pound to get 48 lbs of mixed nuts that sells for $4/pound. How many pounds of each should the merchant

Question 136378: a merchant mix peanuts that sells for $3/pound and cashews that sells for $6/pound to get 48 lbs of mixed nuts that sells for $4/pound. How many pounds of each should the merchant use.
i know this is a system of equations> here is how i proceeded with the problem
x + y = 48
3x+6y= 48, now i am stuck. i am not sure if i even did it right
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Remember the old game when you are trying to find something, and the person who knows where the thing is tells you, "You are getting warmer" or "You are getting colder" as you either get closer or further away from the object? Well, you are so close on this one you are about to burn yourself.

You very properly set x as the unknown number of pounds of peanuts, and y as the unknown number of pounds of cashews, so saying that is absolutely correct because we want to end up with a total of 48lbs of mixed nuts.

You then summed 3x and 6y. 3x represents the cost of the unknown number of pounds of peanuts, because they cost $3 per pound. Likewise, 6y represents the cost of the cashews. But if you are going to add the cost of the peanuts to the cost of the cashews, the result must be the cost of the mixed nuts. You are told that the mixed nuts are to cost $4 per pound, so the total cost of the mixed nuts must be dollars. Therefore your second equation needs to be .

When you do these sorts of problems, it helps to keep the units of measure in mind. x and y are measured in pounds, but 3x and 6y are measured in dollars. So x and y have to add up to a number of pounds, but 3x and 6y have to add up to a number of dollars.

All you have to do now is solve this system of equations and you will have your answer.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
With these type of problems, you have to be able to explain
the reason for the formula, or chances are, you won't get
it right. I like to write the formulas out in words to see
if it makes sense. For this problem:
[(price/lb of peanuts)x(lbs of peanuts)
+ (price/lb of cashews)x(lbs of cashews)] / (48 lbs of mixture) = $4/lb
This makes sense to me, because it's
($ + $)/ lbs = $/lb
Let = pounds of peanuts in mixture
Let = pounds of cashews in mixture

and

Substitute this in the 1st equation

and

The merchant needs 16 pounds of casews and 32 pounds of peanuts
check answer:

OK
Remember, you must understand the formula you are using, or one little
change in the wording of the problem will throw you off
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