Question 120847
Let N = the numerator and D = the denominator, so the fraction can be written as: {{{N/D}}}.
From the problem, you can write:
{{{N = 2D+7}}} so we'll substitute the N with 2D+7 to get:
{{{(2D+7)/D }}} and the reciprocal of this is 0.4, so...
{{{D/(2D+7) = 0.4}}} Replace the 0.4 with its fractional equvalent of {{{4/10}}}
{{{D/(2D+7) = 4/10}}} Now cross-multiply.
{{{10D = 4(2D+7)}}} Simplify and solve for D.
{{{10D = 8D+28}}} Subtract 8D from both sides.
{{{2D = 28}}} Divide both sides by 2.
{{{D = 14}}} and...
{{{N = 2D+7}}}
{{{N = 2(14)+7}}}
{{{N = 35}}}
The original fraction is:
{{{N/D = 35/14}}}