Question 468376
in a certain fraction, the denominator is 4 less than twice the numerator.
 If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4.
 Find the original fraction.
:
Write an equation for each statement
:
"the denominator is 4 less than twice the numerator."
d = 2n - 4
:
"If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4."
{{{(n+15)/(d-15)}}} = 4
n + 15 = 4(d-15)
n + 15 = 4d - 60
n = 4d - 60 - 15
n = 4d - 75
replace d with (2n-4)
n = 4(2n-4) - 75
n = 8n - 16 - 75
n - 8n - 91
91 = 8n - n
91 = 7n
n = {{{91/7}}}
n = 13 is the numerator
then
d = 2(13) - 4
d = 22
:
{{{13/22}}} is the original fraction
:
:
Check this in the statement
"If 15 is added to the numerator and subtracted from the denominator, the value of the fraction is 4."
{{{(13+15)/(22-15)}}} = {{{28/7}}} = 4