Question 563503
Two different schools (A and B) have the same number of pupils.
 The ratio of the boys in school A and the boys in school B is 2:1 and the ratio of the girls in school A and the girls in school B is 4:5.
 Find the ratio of the boys in school A to the girls in school A. 
:
Let Ba = no. of boys in class A
Let Bb = no. of boys in class B
:
Let Ga = no. of girls in class A
Let Gb = no. of girls in class B
:
"Two different schools (A and B) have the same number of pupils."
Ba + Ga = Bb + Gb
:
"The ratio of the boys in school A and the boys in school B is 2:1"
{{{(Ba)/(Bb)}}} = {{{2/1}}}
cross multiply
2Bb = Ba
Bb = .5Ba
:
"and the ratio of the girls in school A and the girls in school B is 4:5."
{{{(Ga)/(Gb)}}} = {{{4/5}}}
cross multiply
4Gb = 5Ga
Gb = {{{5/4}}}Ga
Gb = 1.25Ga
:
We know that: Ba + Ga = Bb + Gb
replace Bb with .5Ba and Gb with 1.25Ga
Ba + Ga = .5Ba + 1.25Ga
Ba - .5Ba = 1.25Ga - Ga
.5Ba = .25Ga
multiply by 4, get rid of the decimals
2Ba = 1Ga
{{{Ba/Ga}}} = {{{1/2}}}
 Find the ratio of the boys in school A to the girls in school A.
1:2, Boys to girls in school A