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Finding the Third Proportional to 97,582 and 213,024

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Solution

The third proportional to 97,582 and 213,024 is: 465,036.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    97,582 : 213,024 = 213,024 : x
  2. Step 2: Convert to fraction form
    97,582/213,024 = 213,024/x
  3. Step 3: Cross multiply
    97,582x = 213,024 × 213,024
  4. Step 4: Simplify right side
    97,582x = 45,379,224,576
  5. Step 5: Solve for x
    x = 45,379,224,576/97,582
  6. Step 6: Final answer
    x = 465,036.84

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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.