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Finding the Third Proportional to 164,057 and 257,021

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Solution

The third proportional to 164,057 and 257,021 is: 402,663.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    164,057 : 257,021 = 257,021 : x
  2. Step 2: Convert to fraction form
    164,057/257,021 = 257,021/x
  3. Step 3: Cross multiply
    164,057x = 257,021 × 257,021
  4. Step 4: Simplify right side
    164,057x = 66,059,794,441
  5. Step 5: Solve for x
    x = 66,059,794,441/164,057
  6. Step 6: Final answer
    x = 402,663.67

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.