Question 241175: Reconciling remainders. Find a positive integer smaller
than 500 that has a remainder of 3 when divided by 5, a
remainder of 6 when divided by 9, and a remainder of 8
when divided by 11.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Reconciling remainders.
Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5,
a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11.
:
we know
x = multiple of 5 + 3, last digit is either 3 or 8
x = multiple of 9 + 6
x = multiple of 11 + 8,
:
Find a multiple of 11 + 8, last digit is 3 or 8
then test to see if it is a multiple of 9 with a remainder 6
:
working downward from 500, I came up with 393
(I used the table on the TI83, with the equation y = 11x + 8, look for last digit of 3 or 8)
:
393/5 = 78 r3
393/9 = 43 r6
393/11= 35 r8
:
There is probably a neater way of doing this but I can't come up with it
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