Question

1. reduced rates three students plan to divide the rent for an apartment equally. when they add a fourth student, the cost per student decreases by $150 per month. what is the total monthly rent for the apartment?

Explanation:

Step1: Define Variables

Let \( R \) be the total monthly rent (in dollars), and let \( c_3 \) be the cost per student when there are 3 students, \( c_4 \) be the cost per student when there are 4 students. We know that \( c_3 - c_4 = 150 \). Also, \( c_3=\frac{R}{3} \) and \( c_4=\frac{R}{4} \) because cost per student is total rent divided by number of students.

Step2: Set Up Equation

Substitute \( c_3 \) and \( c_4 \) into the difference equation:

$$ \frac{R}{3}-\frac{R}{4}=150 $$

Step3: Solve for \( R \)

First, find a common denominator for the left - hand side, which is 12. Then:

$$ \frac{4R}{12}-\frac{3R}{12}=150 $$

Simplify the left - hand side:

$$ \frac{4R - 3R}{12}=150 $$

$$ \frac{R}{12}=150 $$

Multiply both sides by 12 to solve for \( R \):

$$ R = 150\times12=1800 $$

Answer:

The total monthly rent for the apartment is \(\$1800\).