ratio and proportion

[DJHJA]

In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes.
If the ratio of girls to boys in the class is 3:4, then what is the fraction of students in the class having blues eyes?


the answer is 11/70, however the solution given is;

let 1 represent the total # of students
1-(.1+.2)= .7 ( why is this done??? why isnt it .1+.2=.3 as the denominator)

girls(with blue eyes) + boys(with blue eyes) =
(3*.1 )+(4*.2)/ .7 = .3+.8/.7= .11/.7 = 11/70

why is .7 the denominator and not .3.
isnt .3 the total percentage of students with blue eyes?

[Night reader]

In a class, 10% of the girls have blue eyes, and 20% of the boys have blue eyes.
If the ratio of girls to boys in the class is 3:4, then what is the fraction of students in the class having blues eyes?


the answer is 11/70, however the solution given is;

let 1 represent the total # of students
1-(.1+.2)= .7 ( why is this done??? why isnt it .1+.2=.3 as the denominator)

girls(with blue eyes) + boys(with blue eyes) =
(3*.1 )+(4*.2)/ .7 = .3+.8/.7= .11/.7 = 11/70

why is .7 the denominator and not .3.
isnt .3 the total percentage of students with blue eyes?

girls/boys=3/4 => girls/total=3/7 & boys/total=4/7 <=> 3/7 + 4/7 = 1 (girls+boys over total)

blue eyed boys 20% or 1/5
blue eyed girls 10% or 1/10

how many of all boys are blue eyed => 1/5 * 4/7 = 4/35
how many of all girls are blue eyed => 1/10 * 3/7 = 3/70

how many of all boys and girls are blue eyed => 4/35 + 3/70 = 11/70

many OA explanations may differ in notation and decimal translations; we need to know the method only

[DJHJA]

omg thanks ur a life saver

[frank1]

When you see two set of mutually exclusive sets use this method...
it saves time

11/70 clear from it

[ikaplan]

Double matrix method is one of the most useful techniques I have learned during the GMAT prep period. Frank1, thanks for reminding us to use it!