Problema Solution
June has a set of folding chairs. IF she arranges the chairs in rows of 5 with the same number in each row, she has 2 chairs left over. If she arranges them in rows of 3 with the same number, she has 14 left over. How many chairs does she have.
Answer provided by our tutors
Let
'x' represent the number of chairs in each of the 5 rows (when the chairs are placed in 5 rows) then the total number of chairs is: 5x + 2
'y' represent the number of chairs in each of the 3 rows (when the chairs are placed in 3 rows) then the total number of chairs is: 3y + 14
We need to find x and y positive integers such that:
5x + 2 = 3y + 14
5x = 3y + 14 - 2
5x = 3(y + 4)
follows the right hand side must be dividable by 5 while the left hand side is dividable by 3. The equation is satisfied, for example when:
y = 6 and x = 6
thus one solution for the number of chairs is:
5*6 + 2 = 32 = 3*6 + 14
There are 32 chairs.