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G = 9 5 ,
B = 5 Clue
KOLKHOZ IS 120 MILES AWAY FROM THE CITY AND THE TRUCK SHOULD TRAVEL AT 24 MILES AN HOUR. AT 30 MILES PER HOUR A TRUCK TRAVELS A MILE IN 2 MINUTES; AT 20 MILES PER HOUR, IN 3 MINUTES. AT THE LATTER SPEED THE TRUCK IS 1 MINUTE SLOWER PER MILE. TO LOSE 2 HOURS, OR 120 MINUTES, TAKES 120 MILES, WHICH IS HOW FAR THE KOLHOZ IS FROM THE CITY. AT 30 MPH, THE TRUCK WOULD COVER 120 MILES IN 4 HOURS. THE TRIP IS TO TAKE 1 HOUR LONGER, OR TO ARRIVE AT 11:00 A.M., AND CALLS FOR A SPEED OF 24 (120/5) MILES PER HOUR HARISH DELIVERED 95 GLASSES INTACT AND BROKE 5 GLASSES. LET G BE THE NUMBER OF GLASSES DELIVERED INTACT. SO 3G IS THE AMOUNT EARNED FOR DELIVERING THE GLASSES INTACT. LET B BE THE NUMBER OF GLASSES BROKEN. SO 9B IS THE AMOUNT FORFEITED. WE CAN COME UP WITH 2 EQUATIONS: 3G - 9B = 240 G + B = 100 SOLVING THE SIMULTANEOUS EQUATIONS WILL GIVE G=95, B=5 25 EGGS WERE BROKEN. THERE IS ONLY ONE WAY OF FINDING A SOLUTION TO THIS PROBLEM: NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 2: 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 3: 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, 34, 37 NUMBERS WHICH LEAVE A REMAINDER OF 1, WHEN DIVIDED BY 4: 5, 9, 13, 17, 21, 25, 29, 33, 37 NUMBERS WHICH LEAVE NO REMAINDER WHEN DIVIDED BY 5: 5, 10, 15, 20, 25, 30, 35 THE ONLY NUMBER FULFILLING THE FOUR CONDITIONS IS 25 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