Word Problem help

• Dec 13th 2012, 05:54 AM
mjoshua
Word Problem help
At a certain high school, the psychology class consists of 60% of the senior class. In the psychology class, 40% of the students are boys, and there are 90 girls in this class. What is the total number of students in the senior class at this high school?

I know the answer should be 250 but how can I show it algebraically?
• Dec 13th 2012, 06:17 AM
Soroban
Re: Word Problem help
Hello, mjoshua!

Quote:

At a certain high school, the Psychology class consists of 60% of the senior class.
In the Psychology class, 40% of the students are boys, and there are 90 girls in this class.
What is the total number of students in the senior class at this high school?

Let $\displaystyle N$ = total number in the senior class.

60% of $\displaystyle N$ are in the Psych class: .$\displaystyle 0.6N \,=\,P$ .[1]

In the Psych class, 60% are girls: .$\displaystyle 0.6P \,=\,90 \quad\Rightarrow\quad P \,=\,150$ .[2]

Substitute [2] into [1]: .$\displaystyle 0.6N \:=\:150 \quad\Rightarrow\quad N \:=\:\frac{150}{0.6}$

Therefore: .$\displaystyle N \:=\:250$