Question

A certain college has 11,989 students. Assume that 6120 are unemployed sophomores, juniors, or seniors and that 4104 are employed sophomores, juniors, or seniors. There are 745 employed freshmen. Use

for freshmen and
for employed students, and make a Venn diagram marking the number of students in each region of the diagram. How many freshmen are there?

Answer 1

Let's call the number of unemployed sophomores, juniors, or seniors x. Then, the number of employed sophomores, juniors, or seniors is 4104 - x.

From the information given, we know that:

The number of unemployed students (sophomores, juniors, or seniors) is 6120.
The number of employed students (sophomores, juniors, or seniors) is 4104.
So, x + (4104 - x) = 6120

Solving for x, we get:
2104 = 6120

So, there are 2104 unemployed sophomores, juniors, or seniors.

And, 4104 - 2104 = 2000 employed sophomores, juniors, or seniors.

The number of employed students (freshmen and sophomores, juniors, or seniors) is 745 + 4104 = 4849.

The number of students (freshmen, sophomores, juniors, or seniors) is 11,989.

So, the number of employed and unemployed freshmen is 11,989 - 4849 = 7140.

And the number of unemployed freshmen is 7140 - 745 = 6395.

So, there are 6395 unemployed freshmen.

Therefore, the number of freshmen is 6395 + 745 = 7140

Answer 2

Explanation:

Since 4104 students are employed sophomores, juniors, or seniors, the total number of unemployed students is 11,989 - 4104 = 7885.

And since 745 students are employed freshman, the number of unemployed freshman is 7885 - 745 = 7140.

So, the total number of freshman is 745 + 7140 = 7885.

The Venn diagram would look like this:

[ Freshmen ] [ Sophomores, Juniors, Seniors ]

[ 7885 ] __________ [ 4104 ]

| 745 |

__________

[ 7140 ]

So, there are 7885 freshman.