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Finding the Third Proportional to 5,748 and 6,342

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Solution

The third proportional to 5,748 and 6,342 is: 6,997.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,748 : 6,342 = 6,342 : x
  2. Step 2: Convert to fraction form
    5,748/6,342 = 6,342/x
  3. Step 3: Cross multiply
    5,748x = 6,342 × 6,342
  4. Step 4: Simplify right side
    5,748x = 40,220,964
  5. Step 5: Solve for x
    x = 40,220,964/5,748
  6. Step 6: Final answer
    x = 6,997.38

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.