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Finding the Third Proportional to 10,506 and 22,416

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Solution

The third proportional to 10,506 and 22,416 is: 47,827.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,506 : 22,416 = 22,416 : x
  2. Step 2: Convert to fraction form
    10,506/22,416 = 22,416/x
  3. Step 3: Cross multiply
    10,506x = 22,416 × 22,416
  4. Step 4: Simplify right side
    10,506x = 502,477,056
  5. Step 5: Solve for x
    x = 502,477,056/10,506
  6. Step 6: Final answer
    x = 47,827.63

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.