A survey of 1,700 commuters in New York City showed that 1,130 take the subway, 620 take the bus, and 110 do not take either the bus or the subway.
(a)
How many commuters take both the bus and the subway?
To find the number of commuters who take both the bus and the subway, we subtract the number of commuters who only take the subway from the total number of subway commuters, since this group is already accounted for in the number of subway commuters.
The number of subway commuters who do not take only the subway is 1,130 - 110 = <<1130-110=1020>>1,020.
Therefore, 1,020 commuters take both the bus and the subway.
not correct
My apologies for the mistake. To find the number of commuters who take both the bus and the subway, we need to subtract the number of commuters who only take the subway and the number of commuters who only take the bus from the total number of commuters.
Let's denote:
S = number of commuters who take the subway
B = number of commuters who take the bus
The total number of commuters is 1,700, and the number of commuters who do not take either the bus or the subway is 110. So the equation can be written as:
S + B - (110) = 1,700
We also know that 1,130 commuters take the subway and 620 commuters take the bus.
Substituting these values into the equation, we get:
1,130 + 620 - 110 = 1,700
1,750 - 110 = 1,700
1,640 = 1,700
To solve for S + B, we need to subtract the number of commuters who do not take either the bus or the subway from the total number of commuters:
S + B = 1,700 - 110
S + B = 1,590
Therefore, the number of commuters who take both the bus and the subway is 1,590.