College E Students Calculation

The question asks for the total number of students in College E, given specific data about students without low income.

Data for College E

• Percentage of students with low income: 15%
• Percentage of students without low income: $100\% - 15\% = 85\%$
• Proportion of males (M) to females (F) without low income: M:F = 3:2
• Number of males without low income: 2295

Step 1: Calculate Total Students Without Low Income

The proportion 3:2 means that males constitute $\frac{3}{3+2} = \frac{3}{5}$ of the students without low income.

Let $N_{W/O}$ represent the total number of students without low income in College E.

We have the equation:

$ 2295 = \frac{3}{5} \times N_{W/O} $

Solving for $N_{W/O}$:

$ N_{W/O} = 2295 \times \frac{5}{3} $ $ N_{W/O} = 765 \times 5 $ $ N_{W/O} = 3825 $

So, there are 3825 students without low income in College E.

Step 2: Calculate Total Students in College E

Students without low income make up 85% of the total students in College E.

Let $N_{Total}$ represent the total number of students in College E.

We have the equation:

$ N_{W/O} = 85\% \text{ of } N_{Total} $ $ 3825 = 0.85 \times N_{Total} $

Solving for $N_{Total}$:

$ N_{Total} = \frac{3825}{0.85} $ $ N_{Total} = \frac{382500}{85} $ $ N_{Total} = 4500 $

Therefore, the total number of students in College E is 4500.