The denominator of a fraction is four more than twice the numerator. If both numerator and denominator are decreased by nine, the simplified result is 13. Find the original fraction. (Do NOT simplify.)
x / (2 x+4)
(x-9) / (2x-5) = 13
x-9 = 26 x - 65
25 x = 56
x = 56/25
x / (2 x+4) = (56/25 / [ (112/25) + (100 /25) ]
= 56 / 212
To solve this problem, we can follow these steps:
Step 1: Understand the problem:
Let's assume the numerator of the fraction is represented by the variable 'x.' According to the problem, the denominator of the fraction is four more than twice the numerator, which can be represented as "2x + 4."
Step 2: Formulate the equation:
Now, we can set up an equation using the information given in the problem. The fraction can be represented as x/(2x + 4). If we decrease both the numerator and denominator by nine, the simplified result is 13, which can be written as (x - 9)/(2x + 4 - 9) = 13.
Step 3: Simplify the equation:
Simplifying the denominator gives us (x - 9)/(2x - 5) = 13.
Step 4: Solve the equation:
To solve the equation, we can cross-multiply. Multiply 13 on both sides of the equation, which gives us 13(2x - 5) = x - 9.
Expanding and simplifying this equation, we get 26x - 65 = x - 9.
Gather like terms: 26x - x = 65 - 9.
Simplifying further, we have 25x = 56.
Step 5: Solve for x:
Dividing both sides of the equation by 25 gives us x = 56/25.
Therefore, the original fraction is 56/25.