The denominator of a fraction is5 more than the numerator. If the numerator is increased by 18 and the denominator is decreased by 4, the fraction becomes25/8. Find the fraction.
d = n + 5
(n+18)/(n+5-4) = = 25/8
8(n +18) =25 (n+1)
8 n + 144 = 25 n + 25
119 = 17 n
n = 7
d = 7+5 = 12
To solve this problem, let's start by assigning variables to the unknowns. Let's say that the numerator of the fraction is "x" and the denominator is "x + 5" since the denominator is 5 more than the numerator.
According to the problem, if the numerator is increased by 18, we have x + 18, and if the denominator is decreased by 4, we have (x + 5) - 4 = x + 1.
Now, we can set up an equation based on the information given in the problem:
(x + 18) / (x + 1) = 25/8
To get rid of the fractions, we can cross-multiply:
8(x + 18) = 25(x + 1)
Simplifying this equation:
8x + 144 = 25x + 25
Rearranging the equation:
25x - 8x = 144 - 25
17x = 119
Dividing both sides of the equation by 17:
x = 7
So, the numerator of the fraction is 7, and the denominator is 7 + 5 = 12.
Therefore, the fraction is 7/12.