Question

12. The sum of the numerator and denominator of a certain positive fraction is 11. If 1 is added to both the numerator and the denominator, the fraction is increased by 3/56. Find the fraction. ​

Answer 1

Ответ:

хзыдлвлаладададудщуц

Answer 2

Let's assume the numerator of the fraction is represented by the variable "x" and the denominator is represented by the variable "y".

According to the problem, the sum of the numerator and the denominator is 11, so we can write the equation:

x + y = 11 --- (Equation 1)

When 1 is added to both the numerator and the denominator, the new fraction becomes (x+1)/(y+1). It is mentioned that this new fraction is increased by 3/56, so we can write the equation:

(x+1)/(y+1) - x/y = 3/56 --- (Equation 2)

To solve this system of equations, we can simplify Equation 2 by multiplying through by y(y+1) to eliminate the denominators:

y(y+1)(x+1) - xy(y+1) = (3/56)(y(y+1))

Expanding and simplifying Equation 2:

xy + y + x + 1 - xy - xy^2 - xy = (3/56)(y^2 + y)

Simplifying further:

y + x + 1 - xy^2 - xy = (3/56)y^2 + (3/56)y

Now, we can substitute Equation 1 into the simplified Equation 2:

11 + 1 - x(11)^2 - 11x = (3/56)(11^2) + (3/56)(11)

Simplifying further:

12 - 121x - 11x = (3/56)(121) + (3/56)(11)

12 - 132x = (3/56)(121 + 11)

12 - 132x = (3/56)(132)

12 - 132x = 9

-132x = 9 - 12

-132x = -3

x = (-3)/(-132)

x = 1/44

Now that we have the value of x, we can substitute it back into Equation 1 to find the value of y:

1/44 + y = 11

y = 11 - 1/44

y = (484/44) - (1/44)

y = 483/44

Therefore, the fraction is 1/44.