There is a fraction such that if 5 is added to the numerator, its value will be 1/3, and if 7 is subtracted from the denominator, its value will be 1/5. What is the fraction?
Give the answer in the form of fraction.
let the fraction be x/y
(x+5)/y = 1/3
y = 3x + 15
x/(y-7) = 1/5
y - 7 = 5x or y = 5x + 7
so 5x+7 = 3x + 15
2x = 8
x = 4 , then y = 27
the fraction is 4/27
check:
(4+5)/27 = 9/27 = 1/3, check!
4/(27-7) = 4/20 = 1/5 , check!
To find the fraction, we can follow these steps:
Step 1: Let's assume the fraction as "x/y", where x is the numerator, and y is the denominator. So, the fraction can be written as x/y.
Step 2: According to the problem, if 5 is added to the numerator, its value will be 1/3. So, we can write the equation as (x + 5) / y = 1/3.
Step 3: Similarly, if 7 is subtracted from the denominator, its value will be 1/5. So, we can write the equation as x / (y - 7) = 1/5.
Step 4: Now, we have a system of two equations with two variables. We can solve these equations simultaneously to find the values of x and y.
Let's solve these equations:
From equation 1: (x + 5) / y = 1/3
Cross multiplying, we get: 3(x + 5) = y
From equation 2: x / (y - 7) = 1/5
Cross multiplying, we get: 5x = y - 7
Step 5: Now, we have two equations:
3(x + 5) = y
5x = y - 7
Step 6: We can substitute the value of y from the second equation into the first equation:
3(x + 5) = 5x + 7
Step 7: Simplifying the equation:
3x + 15 = 5x + 7
2x = 8
x = 4
Step 8: Substituting the value of x in either of the original equations, we can find the value of y:
5x = y - 7
5(4) = y - 7
20 = y - 7
y = 27
Step 9: Therefore, the fraction is 4/27.