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Finding the Third Proportional to 613 and 659.50

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Solution

The third proportional to 613 and 659.50 is: 709.53

Step by Step Solution

  1. Step 1: Write the proportion equation
    613 : 659.50 = 659.50 : x
  2. Step 2: Convert to fraction form
    613/659.50 = 659.50/x
  3. Step 3: Cross multiply
    613x = 659.50 × 659.50
  4. Step 4: Simplify right side
    613x = 434,940.25
  5. Step 5: Solve for x
    x = 434,940.25/613
  6. Step 6: Final answer
    x = 709.53

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.