Question

June has a set of folding chairs. If she arranges the chairs in 5 rows, she has 2 chairs left over. If she arranges them in 3 rows of the same length, she has 14 left over. How many chairs does she have?

Answer 1

total chairs remain the same
r = chairs in one row

5*r +2 = 3*r + 14 |-3*r

2*r + 2 = 14 |-2
2*r = 12
r= 6

so one row seems to be 6 chairs. we can check if that works in the given problem

"June has a set of folding chairs. If she arranges the chairs in 5 rows, she has 2 chairs left over."
5 * 6 + 2 = 32 chairs, she seems to have that many. and in the second configuration the total must also be 32. or there is something wrong

"If she arranges them in 3 rows of the same length, she has 14 left over."
3*6 + 14 = 18+14 = 20+8+4=32

seems to be right! with 6 chairs per row, the story adds up