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Finding the Third Proportional to 65,309 and 97,710

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Solution

The third proportional to 65,309 and 97,710 is: 146,185.73

Step by Step Solution

  1. Step 1: Write the proportion equation
    65,309 : 97,710 = 97,710 : x
  2. Step 2: Convert to fraction form
    65,309/97,710 = 97,710/x
  3. Step 3: Cross multiply
    65,309x = 97,710 × 97,710
  4. Step 4: Simplify right side
    65,309x = 9,547,244,100
  5. Step 5: Solve for x
    x = 9,547,244,100/65,309
  6. Step 6: Final answer
    x = 146,185.73

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.