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Finding the Third Proportional to 97,700 and 212,896

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Solution

The third proportional to 97,700 and 212,896 is: 463,917.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,700 : 212,896 = 212,896 : x
  2. Step 2: Convert to fraction form
    97,700/212,896 = 212,896/x
  3. Step 3: Cross multiply
    97,700x = 212,896 × 212,896
  4. Step 4: Simplify right side
    97,700x = 45,324,706,816
  5. Step 5: Solve for x
    x = 45,324,706,816/97,700
  6. Step 6: Final answer
    x = 463,917.16

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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.