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Finding the Third Proportional to 14,596 and 21,409

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Solution

The third proportional to 14,596 and 21,409 is: 31,402.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,596 : 21,409 = 21,409 : x
  2. Step 2: Convert to fraction form
    14,596/21,409 = 21,409/x
  3. Step 3: Cross multiply
    14,596x = 21,409 × 21,409
  4. Step 4: Simplify right side
    14,596x = 458,345,281
  5. Step 5: Solve for x
    x = 458,345,281/14,596
  6. Step 6: Final answer
    x = 31,402.12

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.