Liam is setting chairs for meeting he arranges chairs in 5 rows of the same length he has 3 chairs left over if he arranges the chairs in 3 rows of the same lengh he has 21 left over how many chairs does Liam have

Guest Mar 22, 2020

#1**0 **

N mod 5 =3, N mod 3 =2, solve for N

LCM of [3, 5] = 15

N = 8 Number of chairs

15n + 8 = Full solution, where n =0, 1, 2, 3.......etc.

Note: I assumed that arranging the 3 chairs leaves 2 chairs and NOT 21. If the leftover chairs=1, then n = 13 chairs.

Guest Mar 22, 2020

#2**+1 **

Best Answer

Let the row length = L

This implies that, since the number of total chairs is the same in each case, we have

5L + 3 = 3L + 21 subtract 3L, 3 from both sides

2L = 18 divide both sides by 2

L = 9 [ 9 chairs in a row ]

So......the total number of chairs = 5(9) + 3 = 48

CPhill Mar 22, 2020