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Finding the Third Proportional to 209.57 and 313.24

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Solution

The third proportional to 209.57 and 313.24 is: 468.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.57 : 313.24 = 313.24 : x
  2. Step 2: Convert to fraction form
    209.57/313.24 = 313.24/x
  3. Step 3: Cross multiply
    209.57x = 313.24 × 313.24
  4. Step 4: Simplify right side
    209.57x = 98,120.67
  5. Step 5: Solve for x
    x = 98,120.67/209.57
  6. Step 6: Final answer
    x = 468.21

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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.