Some people got on a bus at the terminal. At the first bus stop, half of the people got down and 4 more people got in. Then at the second bus stop, 6 people got down and 8 more got in. If there were a total of 25 people heading to the third stop, how many people got on the bus at the terminal?

Let ' s break down the problem step by step : \n \n 1 . At the third bus stop , there are 2 5 people . \n 2 . Let ' s call the number of people who got on the bus at the terminal " x ". \n 3 . At the first bus stop , half of the people got down , so ( 1 / 2 ) x people got off the bus . \n 4 . Then , 4 more people got on the bus , so the total number of people on the bus is x + 4 . \n 5 . At the second bus stop , 6 people got down , so ( 1 / 2 )( x + 4 ) people got off the bus . \n 6 . Then , 8 more people got on the bus , so the total number of people on the bus is x + 4 + 8 = 2 0 . \n 7 . Since we know that there are 2 5 people at the third bus stop , we can set up an equation to solve for x : x + 4 + 8 = 2 5 . \n 8 . Sol ving for x , we get x = 1 3 . \n \n There fore , there were 1 3 people who got on the bus at the terminal . </s>