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Finding the Third Proportional to 5,706 and 7,707

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Solution

The third proportional to 5,706 and 7,707 is: 10,409.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,706 : 7,707 = 7,707 : x
  2. Step 2: Convert to fraction form
    5,706/7,707 = 7,707/x
  3. Step 3: Cross multiply
    5,706x = 7,707 × 7,707
  4. Step 4: Simplify right side
    5,706x = 59,397,849
  5. Step 5: Solve for x
    x = 59,397,849/5,706
  6. Step 6: Final answer
    x = 10,409.72

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.