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Finding the Third Proportional to 420 and 706.50

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Solution

The third proportional to 420 and 706.50 is: 1,188.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    420 : 706.50 = 706.50 : x
  2. Step 2: Convert to fraction form
    420/706.50 = 706.50/x
  3. Step 3: Cross multiply
    420x = 706.50 × 706.50
  4. Step 4: Simplify right side
    420x = 499,142.25
  5. Step 5: Solve for x
    x = 499,142.25/420
  6. Step 6: Final answer
    x = 1,188.43

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Why These Related Problems?

These problems maintain the same ratio (1.68) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.