The numerator of a fraction is 4 less than the denominator. If 17 is added to each, the value of the fraction is 5/6. Find the original fraction.
"The numerator of a fraction is 4 less than the denominator."
fraction: (d-4)/d
"If 17 is added to each, the value of the fraction is 5/6."
(d-4)+17...5
----------- = --......Use this equation.
.. d+17.....6
d + 13....5
--------- = --
d + 17....6
Cross-multiply.
6(d + 13) = 5(d + 17)
6d + 78 = 5d + 85
6d - 5d = 85 - 78
d = 7 (denominator)
denominator = 7
numerator = 7-4 = 3
fraction: 3/7
check: (3+17)/(7+17) = 20/24 = 5/6
Let x = denominator
((x-4)+17)/(x+17) = 5/6
(x+13)/(x+17) = 5/6
6*(x+13) = 5*(x+17)
6x+78 = 5x+ 85
x = 85 - 78 = 7
ORIGINAL FRACTION...
(x-4)/x = 3/7
3/7
23/27
i think it 3/7
ps sorry but thats fraction work not algebra, algebra is work with letters ie 5a x 2a = 10a
Comments
"The numerator of a fraction is 4 less than the denominator."
fraction: (d-4)/d
"If 17 is added to each, the value of the fraction is 5/6."
(d-4)+17...5
----------- = --......Use this equation.
.. d+17.....6
d + 13....5
--------- = --
d + 17....6
Cross-multiply.
6(d + 13) = 5(d + 17)
6d + 78 = 5d + 85
6d - 5d = 85 - 78
d = 7 (denominator)
denominator = 7
numerator = 7-4 = 3
fraction: 3/7
check: (3+17)/(7+17) = 20/24 = 5/6
Let x = denominator
((x-4)+17)/(x+17) = 5/6
(x+13)/(x+17) = 5/6
6*(x+13) = 5*(x+17)
6x+78 = 5x+ 85
x = 85 - 78 = 7
ORIGINAL FRACTION...
(x-4)/x = 3/7
3/7
23/27
i think it 3/7
ps sorry but thats fraction work not algebra, algebra is work with letters ie 5a x 2a = 10a