Ask a New Question
Menu

Out of the 32 students in Mr. Martin's class, 18 are boys. If this ratio is proportional to the ratio of students in the school and the number of boys in the school, which of the following proportions would best be used to find the number of students in the school? It is given that there are 468 boys in the school..

3 answers

To find the total number of students in the school based on the proportion of boys in Mr. Martin's class, we can set up a proportion based on the information given.

In Mr. Martin's class, there are 32 students total, of which 18 are boys. This gives us the ratio of boys to total students in the class as:

\[ \frac{18 \text{ boys}}{32 \text{ students}} \]

In the school, we know there are 468 boys, and we want to find the total number of students in the school, which we will denote as \( x \). The proportion of boys to total students in the school is:

\[ \frac{468 \text{ boys}}{x \text{ students}} \]

Since the ratios are proportional, we can set up the equation:

\[ \frac{18}{32} = \frac{468}{x} \]

To find \( x \), we can cross-multiply and solve for \( x \):

\[ 18x = 32 \times 468 \]

Now, calculate \( 32 \times 468 \):

\[ 32 \times 468 = 14976 \]

Now we’ve got:

\[ 18x = 14976 \]

Next, isolate \( x \):

\[ x = \frac{14976}{18} = 832 \]

Thus, the total number of students in the school is \( \boxed{832} \).

I didn't want the number, I wanted to know the proportions

I apologize for the misunderstanding! Let's clarify the proportions without solving for the total number of students.

Given the number of boys in Mr. Martin's class and the number of boys in the school, you can set up the proportion as follows:

  1. From Mr. Martin's class:

    • Number of boys: 18
    • Total number of students: 32

    This gives us the ratio: \[ \frac{18}{32} \]

  2. For the entire school, you're given:

    • Number of boys: 468
    • Let \( x \) represent the total number of students in the school.

    Thus, we consider the ratio: \[ \frac{468}{x} \]

Now, the proportions you would use to set up the equation would be:

\[ \frac{18}{32} = \frac{468}{x} \]

This proportion retains the relationship between the number of boys and total students both in Mr. Martin's class and in the school. You can use this proportion to find the total number of students in the school \( x \) if needed.