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
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.
+128407 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
