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Finding the Third Proportional to 657,965 and 964,135

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Solution

The third proportional to 657,965 and 964,135 is: 1,412,774.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    657,965 : 964,135 = 964,135 : x
  2. Step 2: Convert to fraction form
    657,965/964,135 = 964,135/x
  3. Step 3: Cross multiply
    657,965x = 964,135 × 964,135
  4. Step 4: Simplify right side
    657,965x = 929,556,298,225
  5. Step 5: Solve for x
    x = 929,556,298,225/657,965
  6. Step 6: Final answer
    x = 1,412,774.69

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.