Question 1204999
<pre>
          initial      After

Ali         a          5a/8

Baba        b         b+3a/8

Ratio                  1/2
</pre>
{{{(5a/8)/(b+3a/8)=1/2}}}

{{{5a/8=1/2(b+3a/8)}}}

{{{5a/4=b+3a/8}}}

{{{40a/4=8b+3a}}}

{{{10a=8b+3a}}}

{{{7a=8b}}}

{{{7a/(8b)=1}}}

{{{highlight(a/b=8/7)}}}



Might be fewer steps if just multiplied both sides by 8 as the first step.


OR


Alternative Steps in the algebra
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{{{((5a/8)/(b+3a/8))=1/2}}}


{{{(8/8)((5a/8)/(b+3a/8))=1/2}}}

{{{5a/(8b+3a)=1/2}}}

{{{10a=8b+3a}}}

{{{7a=8b}}}

{{{a/b=8/7}}}