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Finding the Third Proportional to 465.19 and 523.69

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Solution

The third proportional to 465.19 and 523.69 is: 589.54

Step by Step Solution

  1. Step 1: Write the proportion equation
    465.19 : 523.69 = 523.69 : x
  2. Step 2: Convert to fraction form
    465.19/523.69 = 523.69/x
  3. Step 3: Cross multiply
    465.19x = 523.69 × 523.69
  4. Step 4: Simplify right side
    465.19x = 274,248.60
  5. Step 5: Solve for x
    x = 274,248.60/465.19
  6. Step 6: Final answer
    x = 589.54

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.