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Finding the Third Proportional to 270.19 and 419.81

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Solution

The third proportional to 270.19 and 419.81 is: 652.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    270.19 : 419.81 = 419.81 : x
  2. Step 2: Convert to fraction form
    270.19/419.81 = 419.81/x
  3. Step 3: Cross multiply
    270.19x = 419.81 × 419.81
  4. Step 4: Simplify right side
    270.19x = 176,242.54
  5. Step 5: Solve for x
    x = 176,242.54/270.19
  6. Step 6: Final answer
    x = 652.30

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.