mixture problem

Question

A silversmith mixed 35 g of an 80% silver alloy with 70 g of a 25% silver alloy. What is the percent concentration of the resulting alloy? (Round your answer to one decimal place.

Answer 1

The amount of silver in

35 g of an 80% silver alloy

35(0.8) = 28 g

70 g of a 25% silver alloy

70(0.25) = 17.5 g

 

The amount of silver in the mixture

28 + 17.5 = 45.5 g

 

The mass of the mixture

35 + 70 = 105 g

 

So the percent concentration of the resulting alloy is

(45.5/105) 100% = 43.3%

 

If you know how to compute weighted averages, you can set up an equation and solve for x.

 

x = [35(80%) + 70(25%)]/(35 + 70) = 43.3%