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Finding the Third Proportional to 314.09 and 420.19

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Solution

The third proportional to 314.09 and 420.19 is: 562.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.09 : 420.19 = 420.19 : x
  2. Step 2: Convert to fraction form
    314.09/420.19 = 420.19/x
  3. Step 3: Cross multiply
    314.09x = 420.19 × 420.19
  4. Step 4: Simplify right side
    314.09x = 176,557.54
  5. Step 5: Solve for x
    x = 176,557.54/314.09
  6. Step 6: Final answer
    x = 562.13

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.