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Finding the Third Proportional to 409.50 and 565.50

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Solution

The third proportional to 409.50 and 565.50 is: 780.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.50 : 565.50 = 565.50 : x
  2. Step 2: Convert to fraction form
    409.50/565.50 = 565.50/x
  3. Step 3: Cross multiply
    409.50x = 565.50 × 565.50
  4. Step 4: Simplify right side
    409.50x = 319,790.25
  5. Step 5: Solve for x
    x = 319,790.25/409.50
  6. Step 6: Final answer
    x = 780.93

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.