In a class of 40 students, 17 have ridden an airplane, 28 have ridden a boat, 10 have ridden in a train, 12 have ridden both anairplane and a boat. 3 have ridden a train only and 4 have ridden an airplane only. Some students in the class have notridden any of the three models of transportation and equal numbers have taken all three.a. How many students have used all the three models of transportation?b. How many students have taken only the boat?

a. To find out how many students have used all three modes of transportation, we need to look at the overlaps. We know that 12 students have ridden both an airplane and a boat. However, this doesn't tell us if these students have also ridden a train. Since it's stated that equal numbers have taken all three, we can assume that the same number of students who have ridden both an airplane and a boat have also ridden a train. Therefore, 12 students have used all three modes of transportation.

b. To find out how many students have taken only the boat, we first need to subtract the students who have ridden all three modes and those who have ridden only the airplane or only the train from the total number of students who have ridden a boat. So, 28 (total number of students who have ridden a boat) - 12 (students who have used all three modes) - 4 (students who have ridden only an airplane) - 3 (students who have ridden only a train) = 9 students have taken only the boat.

a. To find out how many students have used all three models of transportation, we need to look at the overlaps. We know that 12 students have ridden both an airplane and a boat. However, this doesn't tell us if these students have also ridden a train. The problem states that "equal numbers have taken all three" modes of transportation. This means that the number of students who have ridden both an airplane and a boat is the same as the number of students who have ridden all three. Therefore, 12 students have used all three models of transportation.

b. To find out how many students have taken only the boat, we need to subtract the students who have ridden other modes of transportation from the total number of students who have ridden a boat. We know that 28 students have ridden a boat. From these, we subtract the 12 students who have ridden all three modes of transportation, the 4 students who have ridden only an airplane, and the 3 students who have ridden only a train. This gives us 28 - 12 - 4 - 3 = 9 students who have taken only the boat.