Question 1161993: A candy store wishes to mix nuts selling for $2.75 per pound with nuts selling for $4.15
per pound to make a mixture of nuts that can be sold for $3.31 per pound. How many
pounds of nuts of each type should be mixed together to obtain 50 pounds of the mixture
that can be sold for $3.31 per pound?
Found 2 solutions by Alan3354, greenestamps:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! A candy store wishes to mix nuts selling for $2.75 per pound with nuts selling for $4.15 per pound to make a mixture of nuts that can be sold for $3.31 per pound.
How many pounds of nuts of each type should be mixed together to obtain 50 pounds of the mixture that can be sold for $3.31 per pound?
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t = amount of 275
f = amount of 415
----
275t + 415f = 313*50
t + f = 50
--
etc
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is an informal method for solving "mixture" problems like this that will get you to the answer to a problem like this much faster, and with much less work, than the traditional algebraic method outlined by the other tutor.
Obviously, if you mix nuts worth $2.75 per pound with others worth $4.15 per pound, the value of the mixture will be somewhere between $2.75 and $4.15 per pound. The ratio in which the two kinds of nuts are mixed exactly determines the price per pound of the mixture.
And the other way around: the price per pound of the mixture exactly determines the ratio in which the two kinds of nuts are mixed.
Using that concept, solve the problem like this:
(1) Picturing the three prices on a number line, determine what fraction of the distance the price of the mixture is from the lower price to the higher price.
(2) That fraction is the fraction of the mixture that needs to be the higher priced ingredient.
Here are the calculations for solving this problem by that method.
$2.75 to $4.15 is a difference of $1.40
$2.75 to $3.31 is a difference of $0.56
$0.56/$1.40 = 2/5
The price of the mixture is 2/5 of the way from the lower price to the higher price; therefore, 2/5 of the mixture has to be the more expensive nuts.
ANSWER: 2/5 of 50 pounds, or 20 pounds, of the more expensive nuts; the other 30 pounds of the less expensive.
CHECK:
20(4.15)+30(2.75) = 83+82.50 = 165.50
50(3.31) = 165.50
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