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Finding the Third Proportional to 329,072,414,085 and 463,406,473,332

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Solution

The third proportional to 329,072,414,085 and 463,406,473,332 is: 652,578,430,565.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    329,072,414,085 : 463,406,473,332 = 463,406,473,332 : x
  2. Step 2: Convert to fraction form
    329,072,414,085/463,406,473,332 = 463,406,473,332/x
  3. Step 3: Cross multiply
    329,072,414,085x = 463,406,473,332 × 463,406,473,332
  4. Step 4: Simplify right side
    329,072,414,085x = 214,745,559,526,001,638,113,280
  5. Step 5: Solve for x
    x = 214,745,559,526,001,638,113,280/329,072,414,085
  6. Step 6: Final answer
    x = 652,578,430,565.54

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.