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Finding the Third Proportional to 6,214 and 13,586

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Solution

The third proportional to 6,214 and 13,586 is: 29,703.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,214 : 13,586 = 13,586 : x
  2. Step 2: Convert to fraction form
    6,214/13,586 = 13,586/x
  3. Step 3: Cross multiply
    6,214x = 13,586 × 13,586
  4. Step 4: Simplify right side
    6,214x = 184,579,396
  5. Step 5: Solve for x
    x = 184,579,396/6,214
  6. Step 6: Final answer
    x = 29,703.80

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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.