the denominator of a rational number is greater than its numerator BY 7 if the numerator is increased by 17 and the denominator is deacreased by 6 the new number becomes 2 find the orginal number
To solve this problem, let's represent the original rational number as "x."
According to the given information, the denominator of "x" is greater than its numerator by 7. This can be expressed as x = (numerator)/(numerator + 7).
Next, we are told that if we increase the numerator by 17 and decrease the denominator by 6, the new number becomes 2. Therefore, the new rational number can be represented as: (x + 17)/(x + 7 - 6) = 2.
Now, we can solve this equation to find the original number:
(x + 17)/(x + 1) = 2
To remove the fraction, we can cross-multiply:
(x + 17) * 2 = (x + 1) * 1
2x + 34 = x + 1
Next, let's isolate the variable:
2x - x = 1 - 34
x = -33
So, the original number is -33.
original number ---- x/(x+7)
new number: (x+17)/(x+7-6)
= (x+17)/(x+1)
(x+17)/(x+1) = 2
2x + 2 = x+17
x = 15
the original number was 15/22