During the distribution of bonbons to her grandchildren, Grandma Claudia realized that if she distributed 11
chocolates for each of them, 10 candies would remain. In the meantime, distribute 13 chocolates
each of his grandchildren, would lack 6.
Based on this information, it is CORRECT to state that the difference between the number of candies
and the number of grandchildren is
A) 90.
B) 30.
C) -90.
D) -30.
Let n=number of candies,
and c=number of grandchildren
The story expressed in modulo gives the two following equations:
then
mod(n,11)=10 (ten left if each given 11).............(1)
mod(n,13)=-6, or
mod(n,13)=7 (7 left if each given 13)
By enumerating (1), we have
10,21,32,43,54,65,76,87,98,109...
=> 8*11+10=98
By enumerating (2), we have
7,20,33,46,59,72,85,98,101...
=> 8*13-6=98
Hence there are 8 grandchildren and 98 candies.
The difference of the number of candies and the number of grandchildren is therefore 98-8=90.
Another way to get the number of grandchildren is
c=(10-(-6))/(13-11)=8
