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Finding the Third Proportional to 196,902 and 431,946

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Solution

The third proportional to 196,902 and 431,946 is: 947,564.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    196,902 : 431,946 = 431,946 : x
  2. Step 2: Convert to fraction form
    196,902/431,946 = 431,946/x
  3. Step 3: Cross multiply
    196,902x = 431,946 × 431,946
  4. Step 4: Simplify right side
    196,902x = 186,577,346,916
  5. Step 5: Solve for x
    x = 186,577,346,916/196,902
  6. Step 6: Final answer
    x = 947,564.51

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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.