Question 890580
Ratio of the two elements as x:y, assuming based on masses.


Let p = how much of alloy A
Let v = how much of alloy B


Concentration of x in alloy A, {{{5/8}}}
Concentration of y in alloy A, {{{3/8}}}
Concentration of x in alloy B, {{{1/3}}}
Concentration of y in alloy B, {{{2/3}}}


THE MIXTURE TO PREPARE
Concentration of x in mixture, {{{4/7}}}
Concentration of y in mixture, {{{3/7}}}


Account for material x: {{{highlight((5/8)p+(1/3)v=4/7)}}}


Account for material y:  {{{highlight((3/8)p+(2/3)v=3/7)}}}


The "account" equations are a system of two linear equations in two unknowns.  Solve any way you like or know.---------- or, continuing,


Lowest common denominator of those two equations is {{{3*7*8}}}.  Multiplying all members by LCD and simplifying, and solving the two equations will give:
{{{highlight(p=40/49)}}} AND {{{highlight(v=9/49)}}}.
The complete solution is still not finished but this is a long way done for finding the answer to the question,"ratio of the two basic elements in the alloy X".  Knowing p and v, you only know how much of the two alloys to use.
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Actually, you already know the ratio of the two basic elements because they were given in the problem description.  The best question, now answered, was HOW MUCH OF ALLOY A AND ALLOY B to use.  <b>This ratio is 40 parts of A to 9 parts of B.</b>