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Finding the Third Proportional to 465,106 and 697,659

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Solution

The third proportional to 465,106 and 697,659 is: 1,046,488.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    465,106 : 697,659 = 697,659 : x
  2. Step 2: Convert to fraction form
    465,106/697,659 = 697,659/x
  3. Step 3: Cross multiply
    465,106x = 697,659 × 697,659
  4. Step 4: Simplify right side
    465,106x = 486,728,080,281
  5. Step 5: Solve for x
    x = 486,728,080,281/465,106
  6. Step 6: Final answer
    x = 1,046,488.50

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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.