Explanation:
a proportion is a relationship (typically "equal to") between 2 or more ratios.
the idea of proportions is that a ratio can be written in many ways and still be equal to the same value.
remember, a ratio is actually a fraction (with the same handling and transformation rules). it is just differently aligned to 1/1 (the "whole").
in a fraction the denominator (bottom) tells us how many equal parts there are in the whole.
e.g. 5/11 tells us that there are 11 equally large parts, and 5 of them are represented by this fraction.
in a ratio we know how many equally large parts there are in the whole, by adding the numerator and the denominator.
e.g. 5:11 = 5/11 as ratio tells us that there are 5+11 = 16 equally large parts in the whole. these parts then have the same size but different other attributes, and the ratio tells us the relationship (distribution, mixture, ...) between the overall numbers of these types of parts.
like in my example, there could be a class of 32 students, if which 10 are boys and 22 are girls. the gender ratio is then 10/22 or simplified 5/11.
in the last case it means we can create 16 pairs of students, with 5 of these pairs are boys, and 11 of these pairs are girls.
please note, that without the information how many individual units there are in total, the ratio cannot give us any information about that total. it only tells us into how many parts we split the whole to compare the types. but each part can contain multiple individual units. the only sure thing is that every part contains the exact same amount of individual units.
so, in our given problem thankfully we got the ratio (5:6) and the total number of individual units (students) in the whole (class) : 33.
the ratio tells us that we split that whole class into 5+6 = 11 parts (of equal size).
therefore, with 11 parts and 33 total students, we know that each of the 11 parts stands for 33/11 = 3 students.
we know, 5 of these parts represent girls and 6 of these parts represent boys. remember, each part represents 3 students with the same attributes.
therefore, there are
5×3 = 15 girls
6×3 = 18 boys
that already solved this problem.
so, now to the sequence and structure your teacher wants you to do :
x = number of girls in the class.
y = number of boys in the class.
the proportion is now
x:y = 5:6
with the extra knowledge of
x + y = 33
x = 33 - y
we can use that identity in the proportion and solve for y :
(33 - y)/y = 5/6
33 - y = 5y/6
198 - 6y = 5y
11y = 198
y = 198/11 = 18 boys
x = 33 - y = 33 - 18 = 15 girls