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Finding the Third Proportional to 257 and 430

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Solution

The third proportional to 257 and 430 is: 719.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    257 : 430 = 430 : x
  2. Step 2: Convert to fraction form
    257/430 = 430/x
  3. Step 3: Cross multiply
    257x = 430 × 430
  4. Step 4: Simplify right side
    257x = 184,900
  5. Step 5: Solve for x
    x = 184,900/257
  6. Step 6: Final answer
    x = 719.46

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.