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Finding the Third Proportional to 14,564 and 31,854

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Solution

The third proportional to 14,564 and 31,854 is: 69,670.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,564 : 31,854 = 31,854 : x
  2. Step 2: Convert to fraction form
    14,564/31,854 = 31,854/x
  3. Step 3: Cross multiply
    14,564x = 31,854 × 31,854
  4. Step 4: Simplify right side
    14,564x = 1,014,677,316
  5. Step 5: Solve for x
    x = 1,014,677,316/14,564
  6. Step 6: Final answer
    x = 69,670.24

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.