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Finding the Third Proportional to 8,290 and 9,730

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Solution

The third proportional to 8,290 and 9,730 is: 11,420.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,290 : 9,730 = 9,730 : x
  2. Step 2: Convert to fraction form
    8,290/9,730 = 9,730/x
  3. Step 3: Cross multiply
    8,290x = 9,730 × 9,730
  4. Step 4: Simplify right side
    8,290x = 94,672,900
  5. Step 5: Solve for x
    x = 94,672,900/8,290
  6. Step 6: Final answer
    x = 11,420.13

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.