Question 599990
The numerator of a fraction is 2 more than the denominator.
 If denominator is doubled and the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3.
 Find the original fraction.
:
Let x = the denominator
then
(x+2) = the numerator
:
{{{((x+2))/x}}} = the original fraction
:
the equation for the statement:
"If denominator is doubled and the numerator is decreased by 1, the sum of the original fraction and the new one is 7/3."
{{{((x+1))/(2x)}}} + {{{((x+2))/x}}} = {{{7/3}}}
Multiply by 6x
6x*{{{((x+1))/(2x)}}} + 6x*{{{((x+2))/x}}} = 6x*{{{7/3}}}
cancel the denominators and you have
3(x+1) + 6(x+2) = 2x(7)
3x + 3 + 6x + 12 = 14x
9x + 15 = 14x
15 = 14x - 9x
15 = 5x
x = 15/5
x = 3
:
{{{5/3}}} is the original fraction