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Finding the Third Proportional to 209.67 and 313.45

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Solution

The third proportional to 209.67 and 313.45 is: 468.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.67 : 313.45 = 313.45 : x
  2. Step 2: Convert to fraction form
    209.67/313.45 = 313.45/x
  3. Step 3: Cross multiply
    209.67x = 313.45 × 313.45
  4. Step 4: Simplify right side
    209.67x = 98,252.86
  5. Step 5: Solve for x
    x = 98,252.86/209.67
  6. Step 6: Final answer
    x = 468.60

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.