If a number is added to the numerator of \(\frac{4}{9}\) and twice as much is subtracted from the denominator, the result is \(-9\). Find the number.

To find the unknown number added to the numerator of 4/9 and subtracted twice from the denominator that results in -9, we can set up the equation as follows:
Let the number be x. Then, the modified fraction is ((4+x)/(9-2x)) and we know that this fraction equals -9.
The equation to solve is:
(4+x) / (9-2x) = -9
Multiply both sides by (9-2x) to eliminate the denominator:
(4+x) = -9(9-2x)
Expanding the right side gives:
(4+x) = -81 +18x
Moving all terms to one side gives:
18x - x = -81 - 4
17x = -85
Divide both sides by 17 to solve for x:
x = -85/17
x = -5
So, the number is -5.

Answered by LevonHelm | 2024-06-18

The number that needs to be added to the numerator of 9 4 ​ , and twice that number subtracted from the denominator to yield -9 is 5. This was determined by setting up and solving the equation derived from the problem statement. By solving, we find x = 5 .
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Answered by LevonHelm | 2025-01-31