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Finding the Third Proportional to 42,140 and 97,306

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Solution

The third proportional to 42,140 and 97,306 is: 224,690.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    42,140 : 97,306 = 97,306 : x
  2. Step 2: Convert to fraction form
    42,140/97,306 = 97,306/x
  3. Step 3: Cross multiply
    42,140x = 97,306 × 97,306
  4. Step 4: Simplify right side
    42,140x = 9,468,457,636
  5. Step 5: Solve for x
    x = 9,468,457,636/42,140
  6. Step 6: Final answer
    x = 224,690.50

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Why These Related Problems?

These problems maintain the same ratio (2.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.