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Finding the Third Proportional to 320.50 and 412.97

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Solution

The third proportional to 320.50 and 412.97 is: 532.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    320.50 : 412.97 = 412.97 : x
  2. Step 2: Convert to fraction form
    320.50/412.97 = 412.97/x
  3. Step 3: Cross multiply
    320.50x = 412.97 × 412.97
  4. Step 4: Simplify right side
    320.50x = 170,543.19
  5. Step 5: Solve for x
    x = 170,543.19/320.50
  6. Step 6: Final answer
    x = 532.12

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Why These Related Problems?

These problems maintain the same ratio (1.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.