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Finding the Third Proportional to 5,946 and 6,783

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Solution

The third proportional to 5,946 and 6,783 is: 7,737.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,946 : 6,783 = 6,783 : x
  2. Step 2: Convert to fraction form
    5,946/6,783 = 6,783/x
  3. Step 3: Cross multiply
    5,946x = 6,783 × 6,783
  4. Step 4: Simplify right side
    5,946x = 46,009,089
  5. Step 5: Solve for x
    x = 46,009,089/5,946
  6. Step 6: Final answer
    x = 7,737.82

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.