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Finding the Third Proportional to 9,209 and 13,814.50

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Solution

The third proportional to 9,209 and 13,814.50 is: 20,723.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,209 : 13,814.50 = 13,814.50 : x
  2. Step 2: Convert to fraction form
    9,209/13,814.50 = 13,814.50/x
  3. Step 3: Cross multiply
    9,209x = 13,814.50 × 13,814.50
  4. Step 4: Simplify right side
    9,209x = 190,840,410.25
  5. Step 5: Solve for x
    x = 190,840,410.25/9,209
  6. Step 6: Final answer
    x = 20,723.25

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.