Ratios

We can construct the ratio $\frac{x+y}{x-y}=\frac{11}{4}$ . Cross-multiplying gives us $4x+4y=11x-11y$ ; therefore, $7x=15y$ . After further division, this gives us $\frac{y}{x}=\frac{7}{15}$ . Our answer is $7+15=\boxed{22}$ .

We here use the method of componendo and dividendo according to which, if $\frac{x}{y}=\frac{a}{b} \implies \frac{x+y}{x-y}=\frac{a+b}{a-b}$ . Given that, $\frac{x+y}{x-y}=\frac{11}{4}$

It is said that, $\frac{y}{x}=\frac{a}{b}$

$\implies \frac{x}{y}=\frac{b}{a}$

$\implies \frac{x+y}{x-y}=\frac{b+a}{b-a}$

$\implies \frac{11}{4}=\frac{b+a}{b-a}$

$\implies 4b+4a=11b-11a \implies 7b=15a \implies \frac{a}{b}=\frac{7}{15}$

So, now we have $\frac{a}{b}=\frac{7}{15}$ where a and b are coprime, a=7 and b=15, so $a+b=7+15=\boxed{22}$

$4(x+y)=11(x-y)$ $4x+4y=11x-11y$ $15y=7x$ $\frac{y}{x}=\frac{7}{15}$ $a+b=7+15=22$

given that : (x-y) : (x+y) = 11:4

there fore x:y = (11+4 ) : (11-4) ==>x:y = 15 : 7 as given x:y =a : b

we got a=15 and b=7 ==> (a+b)=15+7 = 22 Ans

We can construct the ratio X+Y/X-Y=11/4 . Cross-multiplying gives us ; therefore7X=15Y, . After further division, this gives usY/X=7/15=A/B . Our answer is7+5= .22

x + y = 11 x-y = 4 2x = 15 x = 15/2 Change x by 15/2, the result is 15/2 + y = 11 then y = 7/2 to gain y/x solution: 7/2(under this fraction put a long vinculum) over 15/2 then 7/2 times 2/15 is equals to 7/15. Therefore a + b = 7 + 15 = 22

(x+y)/(x-y)=11/4,

4(x+y)=11(x-y),

15y=7x,

y/x=7/15=a/b,

a+b=7+15= 22

method 1st- applying componendo and dividendo... method 2nd- dividing numetator and denominator of L.H.S. by x.

(x+y)/(x-y) = 11/4 then, (x+y+x-y)/(x+y-x+y) = (11+4)/(11-4) or, 2x/2y=15/7 or x/y=15/7 = b/a so a+b=15+7=22

(x+y)/(x-y)=11/4 Let x/y=p (p+1)/(p-1)=11/4 here after calculaton p=15/7 a/b=15/7 a+b=15+7 =22

y/x=15/7;so a+b=15+7=22

(x+y)/(x-y)=11/4 =>4x+4y=11x-11y =>15y=7x =>y/x=7/15 there fore a+b=7+15=22

Escrevendo a razão de acordo com o que informa o problema:

x+y/x-y = 11/4 4x + 4y = 11x - 11y 15y = 7x

Então:

15/7 = a/b a + b = 15 + 7

Logo, a + b = 22.

(x+y)/(x-y)=11/4 (1+k)/(1-k)=11/4 where k=y/x 4+4k=11-11k 15k=7 k=7/15 therefore a/b=15/7 a+b=22

by componendo and dividendo

x+y/x-y=11/4 4x+4y=11x-11y 7x=15y x/y=15/7 y/x=7/15 a+b=22

by solving the equn x+y =11 x-y=4 we get x=15/2 y=7/2 while writing this in the ratio form we get a/b = 7/15 which corresponds a= 7 and b=15.....therefore a+b =22

If x/y=a/b, then x+y/x-y=a+b/a-b. This is called componendo and dividendo. Use that and you'll get the solution.

Cross multiply equation; find $x$ and $y$ ; find $x\over y$ ; reduce to simplest terms; add; submit.

Given,

$\frac{x + y}{x - y} = \frac{11}{4}$

Since we require $\frac{y}{x}$ , we apply dividendo-componendo ,

$\frac{(x + y) - (x - y)}{(x + y) + (x - y)} = \frac{11 - 4}{11 + 4}$

$\frac{2y}{2x} = \frac{7}{15}$

$\frac{y}{x} = \frac{7}{15}$

Hence, $a + b = 7 + 15 = 22$

That's the answer!

(x + y ) : ( x - y) = 11/4 ---> 4x + 4y = 11x - 11y ---> 15y = 7x ---> y/x = 7/15. So,a + b = 7 + 15 = 22. Answer : 22

(x + y)/(x - y) = 11/4

4x + 4y =11x -11y

7x = 15y

the addition of both coefficient of the unknowns = 22

22

x+Y/x-y +1 =11/4 +1: 2x/x-y = 15/4 -(1) x+y/x-y -1 = 11/4 - 1 ; 2y/x-y = 7/4 -(2) divide (1) by (2) we get x/y =15/7 so a+b= 15+ 7 = 22

x+y/x-y=11/4, 2x/2y=15/7, x/y=15/7=b/a, a+b=15+7=22.