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Finding the Third Proportional to 423 and 465.75

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Solution

The third proportional to 423 and 465.75 is: 512.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    423 : 465.75 = 465.75 : x
  2. Step 2: Convert to fraction form
    423/465.75 = 465.75/x
  3. Step 3: Cross multiply
    423x = 465.75 × 465.75
  4. Step 4: Simplify right side
    423x = 216,923.06
  5. Step 5: Solve for x
    x = 216,923.06/423
  6. Step 6: Final answer
    x = 512.82

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.