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Finding the Third Proportional to 4,205 and 7,783

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Solution

The third proportional to 4,205 and 7,783 is: 14,405.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,205 : 7,783 = 7,783 : x
  2. Step 2: Convert to fraction form
    4,205/7,783 = 7,783/x
  3. Step 3: Cross multiply
    4,205x = 7,783 × 7,783
  4. Step 4: Simplify right side
    4,205x = 60,575,089
  5. Step 5: Solve for x
    x = 60,575,089/4,205
  6. Step 6: Final answer
    x = 14,405.49

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.