SOLUTION: A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.If the same number when divided by 11 leaves remainer m and resulting

Question 1016747: A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively?
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Question:
A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6.If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively?

Solution:
It will be assumed that we work with only positive integers.
"A number when divided by 7 leaves a remainder 3 & the resulting quotient when divided by 11 leaves remainer 6."
Let the number be N=7x+3, then when N is divided by 7, it leaves a remainder of 3.
The resulting quotient (integer part) equals (7x+3)/7=x.
If x/11 leaves a remainder of 6, the smallest value of x is 6, although x could equal 6,17,28,....

If x=6, then N=7*6+3=45.

"If the same number when divided by 11 leaves remainer m and resulting quotient when divided by 7 leaves a remainder n.What are the values of m & n respectively?"

N/11=45/11=4 R1, so m=1.
Quotient=4,
Quotient/7=4/7=0 R4, so n=4

Answer: m=1, n=4 assuming N is the smallest positive value of N=45.

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