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Finding the Third Proportional to 4,190 and 9,854

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Solution

The third proportional to 4,190 and 9,854 is: 23,174.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,190 : 9,854 = 9,854 : x
  2. Step 2: Convert to fraction form
    4,190/9,854 = 9,854/x
  3. Step 3: Cross multiply
    4,190x = 9,854 × 9,854
  4. Step 4: Simplify right side
    4,190x = 97,101,316
  5. Step 5: Solve for x
    x = 97,101,316/4,190
  6. Step 6: Final answer
    x = 23,174.54

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.