Question

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British sterling silver is a copper-silver alloy that is 7.5% copper by weight. How many grams of pure copper and how many grams of British sterling silver should be used to prepare 330 grams of a copper-silver alloy that is 10% copper by weight? (Round your answers to one decimal place.)

British sterling silver ____________ g
Copper ___________g

Answer 1

British sterling silver = 321.1 grams

Copper = 8.9 grams

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Work Shown:

• x = amount of British sterling silver (in grams)
• 330-x = amount of pure copper (in grams)

The two amounts add to 330 grams total. The x is some number in the interval 0 < x < 330.

• 7.5% of x = 0.075x = amount of pure copper from the British sterling
• 0.075x+(330-x) = -0.925x+330 = total amount of pure copper

We want to end up with 330 grams of 10% copper, so we want 0.10*330 = 33 grams of pure copper after mixing the two metals.

Set the 33 equal to the expression -0.925x+330 and solve for x.

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-0.925x+330 = 33

-0.925x = 33-330

-0.925x = -297

x = -297/(-0.925)

x = 321.081 approximately

x = 321.1 when rounding to one decimal place

330-x = 330-321.1 = 8.9

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We'll need 321.1 grams of British sterling silver.

We'll also need 8.9 grams of pure copper.