Question

A university law school accepts 9 out of every 13 applicants. If the school accepted 765 students, find how many applicants they received.

Answer 1

The university law school received applications from approximately 1,105 students.

Step-by-step explanation:

let

�

x be the total number of applicants. The acceptance rate is given as

9

13

13

9

​

, meaning that 9 out of every 13 applicants are accepted. The number of students accepted can be expressed as

9

13

×

�

13

9

​

×x.

Given that the school accepted 765 students, we set up the equation:

9

13

×

�

=

765

13

9

​

×x=765

To find

�

x, we multiply both sides by the reciprocal of

9

13

13

9

​

, which is

13

9

9

13

​

:

�

=

765

×

13

9

≈

1

,

105

x=

9

765×13

​

≈1,105

Therefore, the university law school received applications from approximately 1,105 students.

Understanding acceptance rates and using simple algebraic equations allows us to determine the total number of applicants based on the number of students accepted. This information is valuable for the university to manage admissions processes and assess the level of interest and competition for admission to the law school.

Answer 2

The university law school received 1,105 applicants.

Step-by-step explanation:

To determine the number of applicants, we can set up a proportion based on the acceptance rate. The acceptance rate is 9 out of 13 applicants, meaning 9/13 applicants are accepted. If 9/13 represents the accepted applicants, then 4/13 represents the rejected ones (since 9 accepted + 4 rejected = total applicants).

Given that the school accepted 765 students, we can find the total number of applicants by setting up a proportion:

9/13 = 765/X

To solve for X (total applicants), cross multiply:

9X = 765 * 13

9X = 9945

Then, divide both sides by 9:

X = 9945 / 9

X = 1105

Therefore, the university law school received 1,105 applicants.

This calculation highlights that out of every 13 applicants, 9 were accepted. By using this acceptance rate and the known number of accepted students (765), a proportion was set to find the total number of applicants. Cross-multiplication allowed the equation to be solved, resulting in 1,105 applicants. This approach illustrates how proportions can be used to determine unknown quantities based on established ratios.