Calculus Silver Question

Question

What quantities of silver 84.4% pure and 99.9% pure must be mixed together to give 31.8 grams of silver 93.2% pure? Give your answer to one decimal place.

Quantity of silver 848.4% pure: _____ grams

Quantity of silver 99.99% pure: ______ grams

Answer 1

Let x be the amount of 84.4% silver in grams and y be the amount of 99.9% silver in grams.

Because we have 31.8 grams total,

x + y = 31.8g

The amount of silver in the 84.4% silver quantity is just 84.4% of the number of grams of that substance, or 0.844x. The amount of silver in the 99.9% silver quantity is just 0.999y. Lastly, the total amount of silver would be 31.8g x 93.2% since we have a total of 31.8g of the substance and 93.2% of the substance is silver.

So, we can write an equation:

silver in x + silver in y = total amount of silver

0.844x + 0.999y = 31.8*0.932

So we have the system of equations:

x + y = 31.8

0.844x + 0.999y = 31.8*0.932

Solve for x or y in the first equation and plug back into the second equation

x = 31.8 - y

0.844(31.8 - y) + 0.999y = 31.8*0.932

Solve for y and then plug y back into one of the equations and solve for x