SOLUTION: A nut mixture consists of almonds and cashews. Almonds are $4.45 per pound, and cashews are $6.45 per pound. How many pounds of each type of nut should be mixed to produce 15 lbs s
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-> SOLUTION: A nut mixture consists of almonds and cashews. Almonds are $4.45 per pound, and cashews are $6.45 per pound. How many pounds of each type of nut should be mixed to produce 15 lbs s
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Question 1164273: A nut mixture consists of almonds and cashews. Almonds are $4.45 per pound, and cashews are $6.45 per pound. How many pounds of each type of nut should be mixed to produce 15 lbs selling for $5.25 per pound? Answer by greenestamps(13200) (Show Source):
A typical setup using the usual formal algebraic method:
x pounds of almonds at $4.45 per pound, plus (15-x) pounds of cashews at 6.45 per pound, equals 15 pounds at $5.25 per pound:
The solution uses basic algebra; but some of the calculations are not simple.
I leave it to you to finish the solution using that method.
Here is a quick an easy way to solve two-part mixture problems like this, if a formal algebraic solution is not required.
(1) Picture the three prices on a number line: 4.45, 5.25, and 6.45.
(2) The difference between 4.45 and 6.45 is 2.00; the difference between 4.45 and 5.25 is 0.80. The ratio 0.80/2.00 is 2/5.
(3) So the price per pound of the mixture is 2/5 of the way from the lower price to the higher. That means 2/5 of the mixture has to be the higher priced nuts.
ANSWER: 2/5 of 15 pounds, or 6 pounds, of cashews; the other 9 pounds of almonds.
