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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (Show Source):
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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(52782) About Me  (Show Source):
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.
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 = %281.30%2A175+-+0.90%2A175%29%2F%281.60-0.90%29 = 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  %281.60%2A100+%2B+0.90%2A75%29%2F175 = 1.30 dollars per pound.    ! Correct !

Solved.


Answer by josgarithmetic(39617) About Me  (Show Source):
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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

highlight_green%28L%28M-x%29%2BHx=TM%29

LM-Lx%2BHx=TM
Hx-Lx=TM-LM
%28H-L%29x=TM-LM
highlight%28x=%28TM-LM%29%2F%28H-L%29%29 and other , less expensive nut quantity, M-x.

Substitute your given values and evaluate.

Answer by greenestamps(13200) About Me  (Show Source):
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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.