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Finding the Third Proportional to 5,742 and 6,174

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Solution

The third proportional to 5,742 and 6,174 is: 6,638.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,742 : 6,174 = 6,174 : x
  2. Step 2: Convert to fraction form
    5,742/6,174 = 6,174/x
  3. Step 3: Cross multiply
    5,742x = 6,174 × 6,174
  4. Step 4: Simplify right side
    5,742x = 38,118,276
  5. Step 5: Solve for x
    x = 38,118,276/5,742
  6. Step 6: Final answer
    x = 6,638.50

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.