Final answer:
In the survey, 500 people take both the bus and the subway, and 650 people only take the subway. Calculations are based on the provided figures and accounting for people who take both modes of transport or neither.
Step-by-step explanation:
We can use a Venn diagram to solve this problem, but for this explanation, we will use equations. There are a total of 1500 commuters. We are given that 1150 take the subway, 680 take the bus, and 170 do not take either the bus or the subway.
Part A: How many take both the bus and the subway?
To find the number of people who take both the bus and the subway, we can add the number of subway riders and bus riders, then subtract the total number of commuters and those who don't take either mode of transportation to avoid double counting. So, the calculation is 1150 (subway) + 680 (bus) - 1500 (total commuters) + 170 (neither). Let's denote by B the number of people who take both the bus and the subway:
1150 + 680 - B = 1500 - 170
B = 1150 + 680 - 1500 + 170
B = 500
Therefore, 500 people take both the bus and the subway.
Part B: How many only take the subway?
To find the number of people who only take the subway, we subtract the number of people who take both the bus and the subway from the total number of subway riders:
1150 (total subway riders) - 500 (both bus and subway) = 650
Therefore, 650 people only take the subway.