Question 1190209
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The manager of the Sweet Candy Shop wishes to mix candy worth $4 per pound, $6 per pound, and $10 per pound 
to get 100 pounds of a mixture worth $7.60 per pound. The amount of $10 candy must equal the total amounts 
of the $4 and the $6 candy. How many pounds of each must be used?
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As you read the condition, you understand that the amount of the $10 candy is exactly half of the total 100 pounds, 

i.e. exactly 50 pounds, as well as the combined amount of the $4 and $6 candies is exactly the other half 

of 100 pounds, i.e. 50 pounds.


So, regarding $10 candies, you just know the answer: it is 50 pounds.


To solve for the rest candies, let's assume that the anount of the $6 candies is x pounds;
then the amount of the $4 candies is (50-x) pounds.


Then the cost of the mixture is  6x + 4*(50-x) + 50*10  dollars.


We want it would be 7.60*100 dollars.  So, we write the total cost equation

    6x + 4*(50-x) + 50*10 = 7.60*100.


Simplify and find x


    6x + 200 - 4x + 500 = 760

    6x - 4x = 760 - 500 - 200.

       2x   =       60

        x   =       60/2 = 30.


<U>ANSWER</U>.  Use 30 pounds of the $6 candy;  50-30 = 20 pounds of the $4 candy and 50 pounds of the $10 candy.


<U>CHECK</U>.  The average cost is  {{{(6*30+4*20+10*50)/100}}} = 7.60 dollars per pound.  ! Precisely correct !
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Solved.