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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

Mar 22, 2020

#2
+1

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   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.

Mar 22, 2020
#2
+1

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