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Finding the Third Proportional to 314.88 and 409.94

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Solution

The third proportional to 314.88 and 409.94 is: 533.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.88 : 409.94 = 409.94 : x
  2. Step 2: Convert to fraction form
    314.88/409.94 = 409.94/x
  3. Step 3: Cross multiply
    314.88x = 409.94 × 409.94
  4. Step 4: Simplify right side
    314.88x = 168,048.75
  5. Step 5: Solve for x
    x = 168,048.75/314.88
  6. Step 6: Final answer
    x = 533.70

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.