Question

Imagine you live near a university with a popular basketball team. Every basketball game, you notice that exactly 30% of people take the bus and 70% walk. You also notice that half the people who walk to one game take the bus to the next game. What percentage of those who take the bus to one game, walk to the next game?

Answer 1

To determine the percentage of bus riders who walk to the next basketball game, we use percentages and a simple model.

Step-by-step explanation:

The student's question asks about the percentage of people who take the bus to a basketball game and then walk to the next game. Given that 30% take the bus and 70% walk, and that half of the walkers take the bus to the next game, we want to find the percentage of bus-takers who walk to the next game. We start by noting that since 50% of those who walk take the bus next, then the other 50% continue to walk. Since 70% walk to one game, that means 35% of the total attendees walk to both games.

Now let us consider the bus riders who switch to walking. If we let the total number of attendees be a variable (say 100 for simplicity), then 30 of them take the bus to the first game. If the same proportion of bus riders switch to walking as walkers switch to taking the bus, it would mean that 35% of the bus riders walk the next game, which is 0.35 x 30 = 10.5 people. Hence, the percentage of bus riders who walk to the next game is 10.5 out of 30, which is 35%.