SOLUTION: A grocer wishes to mix some nuts worth $.90 per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.3o per pound. How much of each should sh

Question 1142163: A grocer wishes to mix some nuts worth $.90 per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.3o per pound. How much of each should she use?
Found 4 solutions by Alan3354, ikleyn, josgarithmetic, greenestamps:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A grocer wishes to mix some nuts worth $.90 per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.3o per pound. How much of each should she use?
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n = $0.90 nuts
s = $1.60 nuts
======================
n + s = 175 ---- total weight
90n + 160s = 175*130 ---- total cost
Answer by ikleyn(52786)   (Show Source): You can put this solution on YOUR website!
.

Let "x" be the amount (in pounds) of nuts worth $1.60 per pound. Then the amount of nuts worth $0.90 per pound is the rest (175-x) pounds. The total cost equation is 1.60*x + 0.90*(175-x) = 1.30*175 dollars. From this equation, express x and calculate 1.60x + 0.90*175 - 0.90x = 1.30*175 x = = 100. Answer. 100 pounds at $1.60 and the rest, (175-100) = 75 pounds at $0.90. CHECK. The price per pound of the mixture is then = 1.30 dollars per pound. ! Correct !

Solved.

Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
L, 0.9 dollars per pound
H, 1.6 dollars per pound
T, 1.30 dollars per pound for mixture
M, 175 pound mixture
x, quantity of pounds of the "H" price nuts
M-x, quantity of the "L" nuts

and other , less expensive nut quantity, .

Substitute your given values and evaluate.
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

Try this for an easier and faster way to solve "mixture" problems like this.

(1) 1.30 is 4/7 of the way from 0.90 to 1.60. (0.90 to 1.60 is .70; 0.90 to 1.30 is .40; .40/.70 = 4/7)
(2) Therefore 4/7 of the mixture must be the more expensive nuts.

ANSWER: 4/7 of 175 pounds = 100 pounds of the $1.60 per pound nuts; the rest, 75 pounds, of the $0.90 per pound nuts.

The idea behind this method is that the ratio in which the two ingredients must be mixed is exactly determined (in a linear fashion) by where the target price per pound lies between the per pound prices of the two ingredients.
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