The sum of the numerator and denominator of a fraction is 17. If 3 is added to the numerator, the value of the fraction will be 1. What is the fraction? Explain your workings.
Stop changing your name. Show your own workings
To solve this problem, we need to set up an equation based on the given information.
Let's say the numerator of the fraction is represented by 'x' and the denominator is represented by 'y'. We know that the sum of the numerator and denominator is 17, so we can write the equation:
x + y = 17 (Equation 1)
We are also told that if 3 is added to the numerator, the value of the fraction will be 1. This means that the fraction can be represented as:
(x + 3) / y = 1 (Equation 2)
To solve this system of equations, we can use the method of substitution. We'll solve Equation 1 for 'x' in terms of 'y', and then substitute it into Equation 2.
From Equation 1, we get:
x = 17 - y
Now, substitute this value of 'x' into Equation 2:
(17 - y + 3) / y = 1
Simplifying the equation:
(20 - y) / y = 1
Cross-multiplying:
20 - y = y
Adding 'y' to both sides:
20 = 2y
Dividing by 2:
y = 10
Now that we have the value for 'y', substitute it back into Equation 1 to find 'x':
x + 10 = 17
Subtracting 10 from both sides:
x = 7
So, the numerator is 7 and the denominator is 10. The fraction is 7/10.