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 \( y \).

Let's break it down step by step. Initially, there are 52 passengers on the bus. When \( y \) passengers get off and 4 get on, the number of passengers can be expressed as: \[ 52 - y + 4 = 56 - y \] At the next stop, one-third of the remaining passengers get off. The remaining passengers before this stop is \( 56 - y \). Thus, one-third of \( 56 - y \) is: \[ \frac{1}{3}(56 - y) \] The number of passengers getting off is one-third, so the passengers left after they get off is: \[ 56 - y - \frac{1}{3}(56 - y) + 3 \] Now, let's simplify the expression inside the parentheses: \[ \frac{2}{3}(56 - y) + 3 \] At this point, we know that the total number of passengers after both stops is equal to 25: \[ \frac{2}{3}(56 - y) + 3 = 25 \] Subtract 3 from both sides: \[ \frac{2}{3}(56 - y) = 22 \] Multiplying both sides by \(\frac{3}{2}\) to clear the fraction: \[ 56 - y = 33 \] Thus, solving for \( y \): \[ y = 56 - 33 = 23 \] Therefore, the value of \( y \) is \( \boxed{23} \).