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Finding the Third Proportional to 456.25 and 684.25

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Solution

The third proportional to 456.25 and 684.25 is: 1,026.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    456.25 : 684.25 = 684.25 : x
  2. Step 2: Convert to fraction form
    456.25/684.25 = 684.25/x
  3. Step 3: Cross multiply
    456.25x = 684.25 × 684.25
  4. Step 4: Simplify right side
    456.25x = 468,198.06
  5. Step 5: Solve for x
    x = 468,198.06/456.25
  6. Step 6: Final answer
    x = 1,026.19

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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.