Question 261860
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Let *[tex \Large x] represent the amount of 9 karat gold.  Then *[tex \Large \frac{9}{24}x] represents the amount of pure gold in the unknown amount of 9k gold.  Since the total amount must be 200 grams, then the amount of 18k gold must be *[tex \Large 200\ -\ x], and the amount of pure gold in this amount is *[tex \Large \frac{18}{24}\left(200\ -\ x\right)].  The amount of pure gold in the 200 grams of 14k gold must be *[tex \Large \frac{14}{24}\left(200\right)].  The sum of the two amounts of pure gold in the two quantities to be mixed must equal the amount of pure gold in the mixture, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{9}{24}x\ +\ \frac{18}{24}\left(200\ -\ x\right)\ =\ \frac{14}{24}\left(200\right)]


Solve for *[tex \Large x] to answer the question.  Hint:  First multiply both sides of the equation by 24.


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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