Farmer Hank has fewer than 100 pigs on his farm. If he groups five to a pen, there are always three pigs left over. If he groups the pigs seven to a pen, there is always one left over. However, if he groups the pigs three to a pen, there no pigs left. What is the greatest number of pigs that Farmer Hank could have on his farm?
Mathematics · High School · Mon Jan 18 2021
llm
Answered on
Here, we have to find the common multiple first,
(5a+3) (Remainder = 3): 8 13 18 23 ... 78 83 88 93 98
(7b+1) (Remainder = 1): 8 15 22 29 ... 78 85 92 99
(3c +0) (Remainder = 0): 3 6 9 12 15 ... 78 81 84 87 90 93 96 99 [fewer than 100]
The largest number (but less than 100) in all three lists is 78.