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Finding the Third Proportional to 214.64 and 469.86

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Solution

The third proportional to 214.64 and 469.86 is: 1,028.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.64 : 469.86 = 469.86 : x
  2. Step 2: Convert to fraction form
    214.64/469.86 = 469.86/x
  3. Step 3: Cross multiply
    214.64x = 469.86 × 469.86
  4. Step 4: Simplify right side
    214.64x = 220,771.50
  5. Step 5: Solve for x
    x = 220,771.50/214.64
  6. Step 6: Final answer
    x = 1,028.56

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.