Question

If x:y =3:4,find the ratio of 2x+3y:3x+5y

Answer 1

if x:y=3:5

x:y=3:5

Now we introduce a third variable ‘a’ and we'll find the values of x and y w.r.t a

So, let x=3a and y=5a

Now applying this value of x and y in the given ratio we get

3x+4y:8x+5y

=3(3a)+4(5a):8(3a)+5(5a)

=9a+20a:24a+25a

=29a:49a

=29:49

So the answer is 29:49

Now I'm gonna solve it using the first method. This method needs to be carried out carefully as calculation mistakes are common due to mathematical operations involving fractions.

x:y=3:5

x=3y/5

Applying this in the equation we get

3x+4y:8x+5y

=3(3y/5)+4y:8(3y/5)+5y

=9y/5+4y:24y/55y

=y(9+20)/5:y(24+25)/5

Since both have y and 5 multiplied and divided to it so we can remove them.

So the answer is

29:49

Answer 2

Solution:

$x:y = 3:4\\or, \frac{x}{y} = \frac{3}{4}\\or, \frac{x}{3} = \frac{y}{4} = k (let)\\ \\now, \frac{x}{3} = k                ,       \frac{y}{4}= k\\         or, x =3k                        ,        or, y=4k$

∴

$2x+3y : 3x+5y\\or, 2(3k) +3(4k) : 3(3k)+5(4k)\\or, 6k+12k : 9k+20k\\or, 18k : 29k\\or, 18 : 29$

I hope it helps you.