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Finding the Third Proportional to 210,077 and 314,382

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Solution

The third proportional to 210,077 and 314,382 is: 470,475.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    210,077 : 314,382 = 314,382 : x
  2. Step 2: Convert to fraction form
    210,077/314,382 = 314,382/x
  3. Step 3: Cross multiply
    210,077x = 314,382 × 314,382
  4. Step 4: Simplify right side
    210,077x = 98,836,041,924
  5. Step 5: Solve for x
    x = 98,836,041,924/210,077
  6. Step 6: Final answer
    x = 470,475.31

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.