what is the ratio of a and b if (a+b) to (a-b)=9:4?

Question

with explanation or way to solve

Answer 1

4(a+b) = 9(a-b)
4a+4b=9a-9b
5a=13b
a:b = 13/5

Answer 2

If we get all the a's on one side and all the b's on the other, then we can divide both sides by b to get the
a:b ratio. It will show up as a/b, but that's the same thing. Here we go!
(a+b)/(a-b)=9/4
4(a+b)=9(a-b)
4a+4b=9a-9b
4b+9b=9a-4a
13b=5a
divide both sides by b gives
13 = 5a/b
divide again by 5,
13/5 = a/b
That's it. Good luck!

Answer 3

(a+b)/(a-b) =9/4
so 4(a+b) =9(a-b)
4a+4b= 9a -9b
13b=5a
a/b=13/5 a= (13/5)b

Proof replace a by 13/5b a+b = 18/5 b , a-b = 8/5b
and the ratio is 9/4

Answer 4

Given: (a+b)/(a-b) = 9/4.

Multiply both sides of the equation by 4(a-b).
4a + 4b = 9a - 9b

This yields
5a = 13b

or a/b = 13/5.

Answer 5

This just means
(a+b) ... 9
------- = ---
(a-b) .... 4

So 9(a-b) = 4(a+b) [by cross-multiplication]
9a-9b = 4a+4b
5a = 13b
a/b = 13/5
So a:b = 13:5

You can do this with all ratios... think of them as fractions.

Answer 6

(a+b)/(a-b) = 9/4
or, 4(a+b) = 9(a-b)
or, 4a+4b = 9a-9b
or, 13b = 5a
or, a/b = 13/5

so, a:b = 13:5 [ans]