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Candy selling at $6.00 per pound will be mixed with candy selling at $9.00 per pound. How many pounds of the more expensive candy are needed to produce a 15-pound mixture that sells for $7.00 per pound?

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Jzakoianidn
Let us call X the number of pounds of $6 candies and Y the number of pounds of $9 candies.
We know that:
X+Y=15 (we are picking a total of 15 pounds)
(6X+9Y)/15=7 (the average of each pound out of those 15 is "valued" $7)

So you can deduce that Y=15-X
Then replace Y in the other equation by 15-X which is:
(6X+9*(15-X))/15=7
(6X+135-9X)/15=7
(135-3X)/15=7
135-3X=7*15
135-3X=105
-3X=-30
X=10

So you can deduce that Y=15-10=5

As a matter of fact you can verify that 10 pounds of the first candies are valued $60 and 5 pounds of the seconds are valued $45 which is a total of 105.
105/15=7 which means that the overall 15 pounds do have an average per-pound-value of $7.
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