Question

Let x and y be non-zero numbers. If 2x-3y=0, then (x+3y):(x+2y)=?

Answer 1

\[2x=3y\implies \frac{x}{y}=\frac{3}{2}\]
x+3y:x+2y means
\[\frac{ x+3y }{ x+2y }\] now divide each term by y in this fraction

Answer 2

(x/y + 2y)/(x/y + y)

Answer 3

\[\large\frac{ x+3y }{ x+2y }=\frac{ \frac{x}{y}+\frac{3y}{y} }{\frac{x}{y}+\frac{2y}{y} }=\frac{\frac{x}{y}+3}{\frac{x}{y}+2}\]

Answer 4

now substitute \[\frac{x}{y}=\frac{3}{2}\]

Answer 5

ohh, i miss it

Answer 6

you dont understand?

Answer 7

9/7?
i understand, just calculation mistake

Answer 8

9:7

Answer 9

okay alternatively we cud have put \[x=\frac{3y}{2}\]
then substitute in the equation
\[\frac{ x+3y }{ x+2y }=\frac{ \frac{ 3y }{ 2 } +3y}{ \frac{ 3y }{ 2 }+2y}=\frac{ \frac{ 9 }{ 2 }y }{ \frac{ 7 }{ 2 }y }=\frac{ 9 }{ 7 }\]

Answer 10

ohh i see, thank you