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Finding the Third Proportional to 101,784 and 216,024

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Solution

The third proportional to 101,784 and 216,024 is: 458,484.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    101,784 : 216,024 = 216,024 : x
  2. Step 2: Convert to fraction form
    101,784/216,024 = 216,024/x
  3. Step 3: Cross multiply
    101,784x = 216,024 × 216,024
  4. Step 4: Simplify right side
    101,784x = 46,666,368,576
  5. Step 5: Solve for x
    x = 46,666,368,576/101,784
  6. Step 6: Final answer
    x = 458,484.33

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.