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Finding the Third Proportional to 145,824 and 314,410

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Solution

The third proportional to 145,824 and 314,410 is: 677,896.97

Step by Step Solution

  1. Step 1: Write the proportion equation
    145,824 : 314,410 = 314,410 : x
  2. Step 2: Convert to fraction form
    145,824/314,410 = 314,410/x
  3. Step 3: Cross multiply
    145,824x = 314,410 × 314,410
  4. Step 4: Simplify right side
    145,824x = 98,853,648,100
  5. Step 5: Solve for x
    x = 98,853,648,100/145,824
  6. Step 6: Final answer
    x = 677,896.97

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.