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Finding the Third Proportional to 489 and 830

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Solution

The third proportional to 489 and 830 is: 1,408.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    489 : 830 = 830 : x
  2. Step 2: Convert to fraction form
    489/830 = 830/x
  3. Step 3: Cross multiply
    489x = 830 × 830
  4. Step 4: Simplify right side
    489x = 688,900
  5. Step 5: Solve for x
    x = 688,900/489
  6. Step 6: Final answer
    x = 1,408.79

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These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.