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Finding the Third Proportional to 213,071,723,657 and 463,652,653,174

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Solution

The third proportional to 213,071,723,657 and 463,652,653,174 is: 1,008,926,849,164.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,071,723,657 : 463,652,653,174 = 463,652,653,174 : x
  2. Step 2: Convert to fraction form
    213,071,723,657/463,652,653,174 = 463,652,653,174/x
  3. Step 3: Cross multiply
    213,071,723,657x = 463,652,653,174 × 463,652,653,174
  4. Step 4: Simplify right side
    213,071,723,657x = 214,973,782,795,289,544,884,224
  5. Step 5: Solve for x
    x = 214,973,782,795,289,544,884,224/213,071,723,657
  6. Step 6: Final answer
    x = 1,008,926,849,164.42

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.