Question 1144189
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Given: {{{(1/2)A = (2/3)B}}} [1]<br>
Multiply by 2 to get A in terms of B: {{{A = (4/3)B}}} [2]<br>
The fraction of the cookies that A has is<br>
{{{A/(A+B)}}} [3]<br>
Substitute [2] into [3] and simplify:<br>
{{{A/(A+B) = ((4/3)B/((4/3)B+B)) = ((4/3)B/(7/3)B) = 4/7}}}<br>
That's mathematically sound; but it looks a bit ugly.  Let's see if another path is easier to follow.<br>
Given: {{{(1/2)A = (2/3)B}}}<br>
Multiply by the LCD to clear fractions: {{{3A = 4B}}}<br>
Given that equation, let A = 4x and B=3x.  Then the fraction of the cookies that A has is<br>
{{{A/(A+B) = 4x/(4x+3x) = (4x)/(7x) = 4/7}}}