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Finding the Third Proportional to 272,428 and 409,014

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Solution

The third proportional to 272,428 and 409,014 is: 614,079.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    272,428 : 409,014 = 409,014 : x
  2. Step 2: Convert to fraction form
    272,428/409,014 = 409,014/x
  3. Step 3: Cross multiply
    272,428x = 409,014 × 409,014
  4. Step 4: Simplify right side
    272,428x = 167,292,452,196
  5. Step 5: Solve for x
    x = 167,292,452,196/272,428
  6. Step 6: Final answer
    x = 614,079.51

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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.