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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

Best Answer 

 #2
avatar+111329 
+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

 

 

cool cool cool

 Mar 22, 2020
 #1
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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
avatar+111329 
+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

 

 

cool cool cool

CPhill Mar 22, 2020

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