Question 25151
{{{4/(17+x) = 2/3}}}


Since {{{a/b=c/d}}}means that {{{ad=bc}}}

{{{4/(17+x) = 2/3}}} means that {{{3(4) = 2(17+x)}}}
{{{12 = 34 + 2x}}}


Subtract 34 from each side:
{{{12-34 = 34 -34 +2x }}}
{{{-22 = 2x }}}
{{{-11= x}}}


Check:
{{{4/(17-11) = 4/6 = 2/3}}}
It checks!!



NO EXTRA CHARGE--If the numerator AND denominator of the fraction 4/17 are increase by an amount so that the value of the resulting fraction is 2/13, determine the amount they were increased by.


SOLUTION:  {{{(4+x)/(17+x) = 2/3}}}


Since {{{a/b=c/d}}}means that {{{ad=bc}}}

{{{(4+x)/(17+x) = 2/3}}} means that {{{3(4+x) = 2(17+x)}}}


{{{3(4+x) = 2(17+x)}}}
12+3x = 34 + 2x


Subtract 2x from each side:
12+3x -2x = 34 +2x -2x
12+x = 34


Subtract 12 from each side:
12-12 + x = 34 - 12
x = 22


Check:

{{{(4+22)/(17+22)= 26/39 = 2/3}}}


R^2 at SCC