A marching band wants to line up for their performance. When they line up in threes there are 2 left over. When they line up in fours there are 3 left over. When they line up in fives there are 4 left over. When they line up in sixes there are 5 left over. How many students could there be?

59 students

Step-by-step explanation:

3s+2

5, 8, 11, 14, 17, 20, 23, 26, 29, 32, 35, 38, 41, 44, 47, 50, 53, 56, 59

4s+3

7, 11, 15, 19, 23, 27, 31, 35, 39, 43, 47, 51, 55, 59

5s+4

9, 14, 19, 24, 29, 34, 39, 44, 49, 54, 59

6s+5

11, 17, 23, 29, 35, 41, 47, 53, 59

The smallest number of students there could have been is 59.

answer: the resulting cross section is a rectangle. solution: a plane parallel to the base of a triangular prism will intersect a cross section that is the same shape as its bases. so the cross section is a triangle.

step-by-step explanation: