SOLUTION: Isko wants to mix raisins worth 14 pesos per pound and nuts worth 22 pesos to make 25 pounds of a mixture worth 16 pesos per pound. How many pounds of raisins and how many pounds o

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Question 1099901: Isko wants to mix raisins worth 14 pesos per pound and nuts worth 22 pesos to make 25 pounds of a mixture worth 16 pesos per pound. How many pounds of raisins and how many pounds of nuts should he use? Answer using decimals, rounded off to the hundredths place.
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the amount of raisins (in pounds) to be mix. 

Then the amount of nuts is (25-x) pounds.


x pounds of raisin cost 14x pesos.

(25-x) pounds of nuts cost 22*(25-x) pesos.


The total cost for ingredients is  14x + 22*(25-x).

Isko wants 25 pounds of the mixture cost 16 pesos per pound. In other words,


%2814x+%2B+22%2A%2825-x%29%29%2F25 = 16  pesos per pound.


It is your basic "money" (or "price") equation.


To solve it, multiply both sides by 25. You will get

14x + 22*(25-x) = 16*25,   or

14x + 550 - 22x = 400,   or

-8x = 400 - 550 = 150  ====>  x = %28-150%29%2F%28-8%29 = 18.75.


Answer.  Isko should mix  18.75 pounds of raisins with  25-18.75 = 6.25 pounds of nuts.


Check.   (18.75*14 + 6.25*22)/25 = 16 pesos per pound.  ! Correct !

Solved.