SOLUTION: if a certain no. is added to the numerator and the denominator of 7/9, the result is 5/6. find the number. (use 1 variable thanks)

Question 1144116: if a certain no. is added to the numerator and the denominator of 7/9, the result is 5/6. find the number. (use 1 variable thanks)
Found 2 solutions by Theo, greenestamps:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let x be the number.
(7 + x) / (9 + x) = 5 / 6
cross multiply to get (7 + x) * 6 = (9 + x) * 5.
simplify to get 42 + 6x = 45 + 5x.
subtract 5x from both sides of that tand subtract 42 from both sides of that equation to get x = 3
that's your solution.
(7 + 3) / (9 + 3) = 10 / 12
multiply numerator and denominator of 10 / 12 by (1/2) / (1/2) to get 5 / 6.
solution is confirmed to be good.

Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Your presentation of the problem indicates you want a solution using algebra, and this is a good kind of problem to solve using algebra, as a way to get practice using algebra to solve problems.

But you can also solve it using logical reasoning and a bit of simple arithmetic.

In the given fraction 7/9, the difference between the numerator and denominator is 2. When you add the same number to both numerator and denominator, the difference will still be 2.

So what the question asks you to do is find a fraction equivalent to 5/6 in which the difference between the numerator and denominator is 2.

Since the difference between the numerator and denominator of 5/6 is 1, doubling the numerator and denominator will yield a fraction equivalent to 5/6 in which the difference between the numerator and denominator is 2.

So 5/6 = 10/12. And we see that 10/12 = (7+3)/(9+3); so the number we are looking for is 3.
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