SOLUTION: Two alloys A and B contain gold and silver in the ratio 1:2 and 2:3 .A third alloy C is formed by mixing A and B in the ratio 5:6 .find the percentage of silver in the alloy C.

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Two alloys A and B contain gold and silver in the ratio 1:2 and 2:3 .A third alloy C is formed by mixing A and B in the ratio 5:6 .find the percentage of silver in the alloy C.      Log On


   

Question 697218: Two alloys A and B contain gold and silver in the ratio 1:2 and 2:3 .A third alloy C is formed by mixing A and B in the ratio 5:6 .find the percentage of silver in the alloy C.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I will say that I have +5+ units of A
and +6+ units of B. It doesn't matter
what the unit is.
I mix them to get +11+ units of C.
given:
Let +g+ = units of gold
Let +s+ = units of silver
-------------------------------
For alloy A:
+g%2Fs+=+1%2F2+
+2g+=+s+
+s+=+2g+
--------------
For alloy B:
+g%2Fs+=+2%2F3+
+3g+=+2s+
+s+=+%283%2F2%29%2Ag+
-------------------
Given:
+C+=+A+%2B+B+
+A%2FB+=+5%2F6+
-----------------
For alloy A:
+s+%2B+g+=+5+
+s+=+2g+
+2g+%2B+g+=+5+
+g+=+5%2F3+
+s+=+10%2F3+
---------------
For alloy B:
+s+%2B+g+=+6+
+%283%2F2%29%2Ag+%2B+g+=+6+
+%285%2F2%29%2Ag+=+6+
+g+=+12%2F5+
+s+=+%283%2F2%29%2Ag+
+s+=+18%2F5+
----------------
Adding up the gold, I get
+g+=+5%2F3+%2B+12%2F5+
+g+=+25%2F15+%2B+36%2F15+
+g+=+61%2F15+
Adding up the silver, I get
+s+=+10%2F3+%2B+18%2F5+
+s+=+50%2F15+%2B+54%2F15+
+s+=+104%2F15+
-------------------
I need to find +s+%2F+%28+s+%2B+g+%29+
for alloy C
+s+%2F+%28+s+%2B+g+%29++=+%28+104%2F15+%29+%2F+%28+104%2F15++%2B++61%2F15+%29+
+s+%2F+%28+s+%2B+g+%29+=+104+%2F+%28+104+%2B+61+%29+
+s+%2F+%28+s+%2B+g+%29+=+104+%2F+165+
+s+%2F+%28+s+%2B+g+%29+=+.6333+
The percentage of silver is 63.333 %
------------
check answer:
+.63333%2A11+=+6.93333+ units of silver
+11+-+6.93333+=+4.06666+ units of gold
------------
+g+=+61%2F15+
+61%2F15+=+4.06666+
and
+s+=+104%2F15+
+s+=+6.93333+
OK