8. A bus is travelling with 52 passengers. When it arrives at a stop, $$ y $$ passengers get off and 4 get on. At the next stop one- third of the passengers get off and 3 get on. There are now 25 passengers. Find $$ y $$.

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UpStudy AI · Accepted Answer

To determine the value of $$ y $$, let's break down the problem step by step:

1. **Initial Passengers:**
   - The bus starts with **52 passengers**.

2. **First Stop:**
   - **$$ y $$ passengers get off.**
     - Passengers remaining: $$ 52 - y $$
   - **4 passengers get on.**
     - Total passengers after the first stop: $$ 52 - y + 4 = 56 - y $$

3. **Second Stop:**
   - **One-third of the passengers get off.**
     - Passengers getting off: $$ \frac{1}{3}(56 - y) $$
     - Passengers remaining: $$ (56 - y) - \frac{1}{3}(56 - y) = \frac{2}{3}(56 - y) $$
   - **3 passengers get on.**
     - Total passengers after the second stop: $$ \frac{2}{3}(56 - y) + 3 $$

4. **Final Condition:**
   - After the second stop, there are **25 passengers** on the bus.
     $$
     \frac{2}{3}(56 - y) + 3 = 25
     $$

5. **Solving for $$ y $$:**
   $$
   \frac{2}{3}(56 - y) = 25 - 3
   $$
   $$
   \frac{2}{3}(56 - y) = 22
   $$
   $$
   56 - y = 22 \times \frac{3}{2}
   $$
   $$
   56 - y = 33
   $$
   $$
   y = 56 - 33
   $$
   $$
   y = 23
   $$

**Final Answer:**  
$$ y = 23 $$
$$ y = 23 $$

A bus is travelling with 52 passengers. When it arrives at a
stop, passengers get off and 4 get on. At the next stop one-
third of the passengers get off and 3 get on. There are now
25 passengers. Find .

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A bus is travelling with 52 passengers. When it arrives at a stop, passengers get off and 4 get on. At the next stop one- third of the passengers get off and 3 get on. There are now 25 passengers. Find .