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Finding the Third Proportional to 302.25 and 414.75

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Solution

The third proportional to 302.25 and 414.75 is: 569.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    302.25 : 414.75 = 414.75 : x
  2. Step 2: Convert to fraction form
    302.25/414.75 = 414.75/x
  3. Step 3: Cross multiply
    302.25x = 414.75 × 414.75
  4. Step 4: Simplify right side
    302.25x = 172,017.56
  5. Step 5: Solve for x
    x = 172,017.56/302.25
  6. Step 6: Final answer
    x = 569.12

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Why These Related Problems?

These problems maintain the same ratio (1.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.