Question

If the ratio of x+y to x−y is 114, then the ratio of y to x can be written as ab where a and b are coprime positive integers. Find a+b.

Answer 1

I think you mean 11/4 right...

Here, I'll help you, but I want you to solve the problem in the end. The key is simplification.

You have x+y = 11 ... and x-y = 4 If you put the two equations together you'll get Y. If you submit y into the original equation you'll get x and the summation of that will be your final answer. Sorry I know the answer but I don't want to answer it for you. Have a go at it at least... I know you can do it! ;)

Answer 2

So David, you mean,

x + y = 11
x - y = 4

x = 7.5
y = 3.5

Then we need to substitute y into the original equation?

x + 3.5 = 11
x = 7.5
x - 3.5 = 4
x = 7.5

Adding the values lead x = 15?

Answer 3

Nope... I had it wrong... And I know I was a hypocrite there for a sec! :)


Solution 1: By componendo and dividendo, we get that (x+y)−(x−y)/(x+y)+(x−y)=11−4/11+4=715. Hence, yx=715, so a+b=22.

Solution 2: Since the ratio of x+y to x−y is 114, we can write
x+y/x−y=114.
We cross-multiply to get rid of the fractions and get 4(x+y)=11(x−y). Distributing the constants into the parentheses gives us 4x+4y=11x−11y. Adding 11y to both sides and subtracting 4x from both sides of this equation gives us 15y=7x. Now in order to find the ratio of y to x, we divide both sides by 15 and by x to obtain yx=7/15. (Note that we can divide by x, since we know x≠0 from the given x+y/x−y=11/4.)

Therefore, the ratio of y to x is 7/15. So a=7 and b=15, hence a+b=22.


The Answer is 22

Answer 4

I guess then you had part of it right...