The denominator of a fraction exceeds the numerator by 7. If 3 is added to the numerator and 1 is subtracted from the denominator, the resulting fraction is equal to 4/5 . Find the original fraction.
PLZ SHOW ALL WORK AND HURRY!!!
let the numerator be x
then the denominator is x+7
3 is added to the numerator, so the new numerator is ......
1 is subtracted from x+7 , so the new denominator is ......
the new fraction is ???/????
???/???? = 4/5
solve for x
show me your steps, so I can check it
To solve this problem, let's first set up the equations based on the given information:
Let the numerator of the original fraction be x.
The denominator of the original fraction will then be x + 7.
After adding 3 to the numerator and subtracting 1 from the denominator, the resulting fraction becomes:
(x + 3) / (x + 7 - 1) = 4/5
Now, let's simplify the equation and solve for x:
(x + 3) / (x + 6) = 4/5
To eliminate the fractions, we can cross-multiply:
5(x + 3) = 4(x + 6)
Expand the equation:
5x + 15 = 4x + 24
Subtract 4x from both sides:
5x - 4x + 15 = 24
Simplify:
x + 15 = 24
Subtract 15 from both sides:
x = 9
So, the numerator of the original fraction is 9.
Now, substitute the value of x into the equation for the numerator:
Numerator = x = 9
And substitute x + 7 for the denominator:
Denominator = x + 7 = 9 + 7 = 16
Therefore, the original fraction is 9/16.