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Finding the Third Proportional to 293,989 and 414,013

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Solution

The third proportional to 293,989 and 414,013 is: 583,038.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    293,989 : 414,013 = 414,013 : x
  2. Step 2: Convert to fraction form
    293,989/414,013 = 414,013/x
  3. Step 3: Cross multiply
    293,989x = 414,013 × 414,013
  4. Step 4: Simplify right side
    293,989x = 171,406,764,169
  5. Step 5: Solve for x
    x = 171,406,764,169/293,989
  6. Step 6: Final answer
    x = 583,038.02

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.