If a certain number is added to the numerator and denominator of 5/11, the result is 5/8. Find the number.
(5+x)/(11+x) = 5/8
so solve for x.
To solve this problem, let's break it down step by step:
Step 1: Understanding the problem
The problem states that if a certain number is added to both the numerator and denominator of the fraction 5/11, the result is 5/8.
Step 2: Set up the equation
Let's assign a variable, let's say "x", to represent the certain number that needs to be added to both the numerator and denominator.
The equation can be written as: (5 + x) / (11 + x) = 5/8
Step 3: Cross-multiply and simplify
To solve the equation, cross-multiply the fractions.
8 * (5 + x) = 5 * (11 + x)
Simplify both sides of the equation:
40 + 8x = 55 + 5x
Step 4: Isolate the variable
In order to solve for "x", we need to isolate the variable on one side of the equation.
Subtract 5x from both sides:
3x = 55 - 40
Combine like terms:
3x = 15
Step 5: Solve for the variable
To find the value of "x", divide both sides of the equation by 3:
x = 15/3
Simplify the division:
x = 5
Step 6: Answer the question
Therefore, the number that needs to be added to both the numerator and the denominator of 5/11 is 5.