Pre-Calculus

Question

Dayton's Metal's has three silver alloys on hand. One has 22% silver, another is 30% silver, and the third is 42% silver. How many grams of each alloy is required to produce 80 grams of new alloy that is 34% silver if the amount of 30% alloy used is twice the amount of 22% alloy used.

Answer 1

Say,

x gms of 22% silver

y gms of 30% silver

z gms of 42% silver

 

So, as per data given,

 

x + y + z=80

y =2x

22x+30y+42z=34x+34y+34z

Or

12x+4y-8z=0

Or

5x-2z=0

3x+z=80

 

Solving the above equations

 

x =14.54 gms

y =29.08 GMS

z=36.38   gms