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Finding the Third Proportional to 322.50 and 509.50

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Solution

The third proportional to 322.50 and 509.50 is: 804.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    322.50 : 509.50 = 509.50 : x
  2. Step 2: Convert to fraction form
    322.50/509.50 = 509.50/x
  3. Step 3: Cross multiply
    322.50x = 509.50 × 509.50
  4. Step 4: Simplify right side
    322.50x = 259,590.25
  5. Step 5: Solve for x
    x = 259,590.25/322.50
  6. Step 6: Final answer
    x = 804.93

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.