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Finding the Third Proportional to 39,822 and 83,478

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Solution

The third proportional to 39,822 and 83,478 is: 174,993.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    39,822 : 83,478 = 83,478 : x
  2. Step 2: Convert to fraction form
    39,822/83,478 = 83,478/x
  3. Step 3: Cross multiply
    39,822x = 83,478 × 83,478
  4. Step 4: Simplify right side
    39,822x = 6,968,576,484
  5. Step 5: Solve for x
    x = 6,968,576,484/39,822
  6. Step 6: Final answer
    x = 174,993.13

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.