Three students are planning to rent an apartment for a year and share equally in the cost. By adding a fourth person, each person could save $75 a month. How much is the monthly rent?

C/3-C/4=75

Solve for C.

,m.k

To determine the monthly rent, we need to solve the problem using algebra. Let's denote the monthly rent as "R".

According to the information given, if there are three students sharing the cost equally, each student would be paying (1/3) of the total rent. Therefore, the cost per person is (1/3)R.

If a fourth person joins, each person would then pay (1/4) of the total rent. We are told that each person could save $75 a month if there is a fourth person, which means that each person's new cost would be reduced by $75.

So, we can set up the equation:

(1/3)R - (1/4)R = $75

To solve this equation, we'll find a common denominator for 3 and 4, which is 12:

(4/12)R - (3/12)R = $75

Now, we can combine the like terms:

(1/12)R = $75

To isolate R, we'll multiply both sides of the equation by 12:

(1/12)R * 12 = $75 * 12

R = $900

Therefore, the monthly rent is $900.