If the ratio of x+y to x−y is 11/4, then the ratio of y to x can be written as a/b where a and b are coprime positive integers. Find a+b .
To find the ratio of y to x, we can use the given ratio of (x+y) to (x-y) and express it in terms of y and x.
Given: (x+y)/(x-y) = 11/4
Now, cross multiply to get rid of the denominator:
4(x+y) = 11(x-y)
Expanding the equation, we get:
4x + 4y = 11x - 11y
Now, let's collect the terms with x on one side and the terms with y on the other side:
11x - 4x = 11y + 4y
7x = 15y
To find the ratio of y to x, we can rewrite the equation as:
y/x = 7/15
Therefore, the ratio of y to x is 7/15.
Since 7 and 15 are already coprime, the sum of a and b is 7 + 15 = 22.
Hence, a+b = 22.