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Finding the Third Proportional to 500.75 and 824.50

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Solution

The third proportional to 500.75 and 824.50 is: 1,357.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    500.75 : 824.50 = 824.50 : x
  2. Step 2: Convert to fraction form
    500.75/824.50 = 824.50/x
  3. Step 3: Cross multiply
    500.75x = 824.50 × 824.50
  4. Step 4: Simplify right side
    500.75x = 679,800.25
  5. Step 5: Solve for x
    x = 679,800.25/500.75
  6. Step 6: Final answer
    x = 1,357.56

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.