J _ M
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7
_ N D
5
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I F
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J = 7
_ N D
W = 5 Clue
SHE NEEDS TO GIVE YOU 5 APPLES. YOU BOTH NEED AT LEAST 5 APPLES TO BEGIN WITH, BUT APART FROM THAT IT DOESN'T MATTER EXACTLY HOW MANY YOU EACH HAVE. WHEN SHE GIVES YOU 5 YOU WILL HAVE 10 MORE THAN HER BECAUSE SHE WILL LOSE 5 AND YOU WILL GAIN 5, RESULTING IN A NET DIFFERENCE OF 10. FOR EXAMPLE, IF BOTH OF YOU HAVE 20 APPLES AND SHE GIVES YOU 5 OF HERS, SHE WILL BE LEFT WITH 15 AND YOU WILL NOW HAVE 25, PRECISELY 10 MORE THAN SHE HAS YOU CAN GET 833 APPLES TO BANANAVILLE. FIRST YOU HAVE TO MAKE 3 TRIPS OF 1,000 APPLES FOR 333 MILES. YOU WILL BE LEFT WITH 2,001 APPLES AND 667 MILES TO GO. NEXT YOU HAVE TO TAKE 2 TRIPS OF 1,000 APPLES FOR 500 MILES. YOU WILL BE LEFT WITH 1,000 APPLES AND 167 MILES TO GO (YOU HAVE TO LEAVE AN APPLE BEHIND). FINALLY, YOU TRAVEL THE LAST 167 MILES WITH ONE LOAD OF 1,000 APPLES AND ARE LEFT WITH 833 APPLES IN BANANAVILLE YOU NEED TO TAKE OUT THREE SOCKS. TO HAVE A MATCHING PAIR, YOU NEED TO TAKE 2 SOCKS THAT ARE OF THE SAME COLOR. WHEN YOU TAKE 3 SOCKS, 2 OF THE SOCKS WILL BE OF THE SAME COLOR JIM AND WANDA HAVE 7 AND 5 APPLES RESPECTIVELY. TO SOLVE USING MATHS, LET J AND W BE THE NUMBER OF APPLES OF JIM AND WANDA RESPECTIVELY. IF JIM GIVES WANDA AN APPLE, THEY WILL BOTH HAVE THE SAME NUMBER OF APPLES: W + 1 = J - 1 IF WANDA GIVES JIM AN APPLE, JIM WILL HAVE TWICE AS MANY AS WANDA: 2(W - 1) = J + 1 SOLVING THE EQUATIONS WILL GIVE J=7 AND W=5