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Finding the Third Proportional to 509.75 and 561.75

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Solution

The third proportional to 509.75 and 561.75 is: 619.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    509.75 : 561.75 = 561.75 : x
  2. Step 2: Convert to fraction form
    509.75/561.75 = 561.75/x
  3. Step 3: Cross multiply
    509.75x = 561.75 × 561.75
  4. Step 4: Simplify right side
    509.75x = 315,563.06
  5. Step 5: Solve for x
    x = 315,563.06/509.75
  6. Step 6: Final answer
    x = 619.05

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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.