need help please!!

Let b be the number of boys and g be the number of girls originally.

$(1+35\%)b=(1+10\%)g\\ \dfrac{b}{g}=\dfrac{(1+10\%)}{(1+35\%)}=\dfrac{1.1}{1.35}=\dfrac{22}{27}\\ \therefore b:g = 22:27$

I divided (1+35%)g on each side of Step 1 so I get step 2. Then I simplify the fraction on the right hand side of the equal sign to make the numerator and denominator both integers. Then I used the definition of ratio to get the conclusion.

The definition: $x:y = \dfrac{x}{y}$

Sorry wrong equation.

$(1+35\%)b=(1-10\%)g\\ \dfrac{b}{g}=\dfrac{(1-10\%)}{(1+35\%)}=\dfrac{0.9}{1.35}=\dfrac{2}{3}\\ \therefore b:g = 2:3$

Same steps as the wrong equation. My mistake is just turned 1-10% into 1+10%.