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Finding the Third Proportional to 53,506 and 82,964

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Solution

The third proportional to 53,506 and 82,964 is: 128,640.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    53,506 : 82,964 = 82,964 : x
  2. Step 2: Convert to fraction form
    53,506/82,964 = 82,964/x
  3. Step 3: Cross multiply
    53,506x = 82,964 × 82,964
  4. Step 4: Simplify right side
    53,506x = 6,883,025,296
  5. Step 5: Solve for x
    x = 6,883,025,296/53,506
  6. Step 6: Final answer
    x = 128,640.25

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.