SAT question of the day Nov 08 2012
In a class of seniors, there are boys for every girls. In the junior class, there are boys for every girls. If the two classes combined have an equal number of boys and girls, how many students are in the junior class?
First lets identify the type of question we have. Reading the question it is clear we have a ratio problem (boys to girls) with the sub-category of mixing problems – you take one class with a certain ratio, mix it with another and get a new ratio.
We now have to decide what would be the best strategy to solve. Lets consider the information.
Class I – the senior class – has 80 students with a 3:5 boys to girls. This implies that out of every 8 students (3+5) 3 are boys and 5 are girls. This mean there are 30 boys and 50 girls in this class.
Class II- the junior class – has ? number of students with 2 girls for every 3 boys or 3:2 boys to girls. We don’t know how many students are in the junior class and actually this is the number we are looking for as our answer.
What else do we know? We know that when mixed together the resulting population has a 1:1 ratio of boys to girls or equal number of boys and girls.
Several possible ways to solve.
One – write an equation – if X is the number of students in the junior class then the number of boys in the class is 3/5 of X and the number of girls is 2/5 of X.
That means that in the combined class the number of all the boys is 30 + (3/5)*X and the number of girls is 50+ (2/5)*X. However these two expressions are equal !
We then write an equation: 30 + (3/5)*X = 50+ (2/5)*X or when simplified (1/5)*X=20 and then X=100
Two – plug in. We know that the junior class has a ratio of 3:2 – it will make sense then that the total number of students in the junior class will be a multiplicity of 5 (answers A and C can be ignored). If we plug in 80 we have 48 boys and 32 girls – but we need a difference of 20 to account for the excess girls in the senior class. If we check 120 we get 72 boys and 48 girls – too many. You can see the 100 is the correct answer – plug in is a legitimate option, wise plug in is even better.
Three – If you understand that the junior class should have 20 more boys than girls and that these 20 boys are 1/5 of the class because there are 3/5 boys and only 2/5 girls in the junior class – it is straight forward to find the answer – 100 students in the junior class.