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Finding the Third Proportional to 464.65 and 684.14

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Solution

The third proportional to 464.65 and 684.14 is: 1,007.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    464.65 : 684.14 = 684.14 : x
  2. Step 2: Convert to fraction form
    464.65/684.14 = 684.14/x
  3. Step 3: Cross multiply
    464.65x = 684.14 × 684.14
  4. Step 4: Simplify right side
    464.65x = 468,050.40
  5. Step 5: Solve for x
    x = 468,050.40/464.65
  6. Step 6: Final answer
    x = 1,007.32

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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.