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1972 AMC 12 Question 34

AMC12 · 1972 AMC 12

Question 34

Three times Dick’s age plus Tom’s age equals twice Harry’s age. Double the cube of Harry’s age is equal to three times the cube of Dick’s age added to the cube of Tom’s age. Their respective ages are relatively prime to each other. The sum of the squares of their ages is:
  1. $42$
  2. $46$
  3. $122$
  4. $290$
  5. $326$