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Finding the Third Proportional to 423.42 and 456.19

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Solution

The third proportional to 423.42 and 456.19 is: 491.49

Step by Step Solution

  1. Step 1: Write the proportion equation
    423.42 : 456.19 = 456.19 : x
  2. Step 2: Convert to fraction form
    423.42/456.19 = 456.19/x
  3. Step 3: Cross multiply
    423.42x = 456.19 × 456.19
  4. Step 4: Simplify right side
    423.42x = 208,107.04
  5. Step 5: Solve for x
    x = 208,107.04/423.42
  6. Step 6: Final answer
    x = 491.49

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.