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Finding the Third Proportional to 205,643 and 311,057

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Solution

The third proportional to 205,643 and 311,057 is: 470,506.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,643 : 311,057 = 311,057 : x
  2. Step 2: Convert to fraction form
    205,643/311,057 = 311,057/x
  3. Step 3: Cross multiply
    205,643x = 311,057 × 311,057
  4. Step 4: Simplify right side
    205,643x = 96,756,457,249
  5. Step 5: Solve for x
    x = 96,756,457,249/205,643
  6. Step 6: Final answer
    x = 470,506.93

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.