SOLUTION: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the or
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Question 1036683: The denominator of a fraction is four less than twice the numerator if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. What is the original fraction?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let n = the numerator of the original fraction
let d = the denominator
:
Write an equation for each statement
:
The denominator of a fraction is four less than twice the numerator
d = 2n - 4
:
if three is added to both the numerator and denominator, the new fraction is equal to two-thirds.
=
cross multiply
3(n+3) = 2(d+3)
3n + 9 = 2d + 6
3n = 2d + 6 - 9
3n = 2d - 3
replace d = (2n-4)
3n = 2(2n-4) - 3
3n = 4n - 8 - 3
3n - 4n = -11
-n = -11
n = 11
Find d using the 1st equation d = 2n - 4
d = 2(11) - 4
d = 18
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What is the original fraction?
:
:
You can check this for yourself, in the statement
"if three is added to both the numerator and denominator, the new fraction is equal to two-thirds. "
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