In Psychology 101, the ratio of the number of girls to the number of boys is $3:2$. After seven more girls join the class, and two boys drop the class, the ratio of the number of girls to the number of boys becomes $5:2$. How many students are in the class after these changes?

35

Step-by-step explanation:

At the beginning, the ratio number of girls : number of boys is

(1)

where

G is the number of girls

B is the number of boys

Later, seven more girls join the class, and two boys drop the class, so the new numbers of girls and boys are

and

We are also told that now the ratio is

Substituting the two equations above,

(2)

Also, from eq.(1) we can write

And substituting into (2) and re-arranging, we can find B:

And so

Therefore, the total number of students in the class BEFORE is

And so, after we have:

So the new number of students is

answer for #1 is c

answer for #2 is d

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step-by-step explanation: