SOLUTION: Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ?

Algebra ->  Real-numbers -> SOLUTION: Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ?      Log On


   

Question 1045027: Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
red%28EDITED%29 red%28SOLUTION%29 (Sorry about the typo):
We are told that
number%5B1%5D=divisor%2Aquotient%5B1%5D%2B11 , and
number%5B2%5D=divisor%2Aquotient%5B2%5D%2B21 .
So, adding up those two equations, we get

number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32
Since we are also told that
number%5B1%5D%2Bnumber%5B2%5D=divisor%2Aquotient%5B3%5D%2B4 ,
subtracting from the equation above from
number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32
we get
0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29%2B4-32
0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29-28
28=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29
Since all the numbers involved in that equation are integers,
that tells us that divisor is a factor of 28 ,
and it has to be a factor larger than 21 ,
because red%28cross%2828%29%2921 was a remainder,
and remainders are always smaller than their divisor.
The only factor of 28 that is greater than 21 is 28 ,
so highlight%2828%29 is the divisor.