When nine is added to both the numerator and the denominator of an original fraction, the new fraction equals six sevenths. When seven is subtracted from both the numerator and the denominator of the original fraction, a third fraction is two thirds. Find the original fraction.

Question

Use algebraic equations to justify your answer.

Answer 1

Just put the words into symbols. If the original fraction is n/d, then

(n+9)/(d+9) = 6/7
(n-7)/(d-7) = 2/3

Now just solve for n and d.

Answer 2

I'm not really sure how I'm supposed to solve for n or d.

Answer 3

as usual, first just clear fractions:

(n+9)(7) = 6(d+9)
(n-7)(3) = 2(d-7)

7n+63 = 6d+54
3n-21 = 2d-14

7n-6d = -9
3n-2d = 7

Now can you solve for n and d?

Answer 4

15/19

Answer 5

isnt it 1/2