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Finding the Third Proportional to 82,284 and 180,288

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Solution

The third proportional to 82,284 and 180,288 is: 395,019.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,284 : 180,288 = 180,288 : x
  2. Step 2: Convert to fraction form
    82,284/180,288 = 180,288/x
  3. Step 3: Cross multiply
    82,284x = 180,288 × 180,288
  4. Step 4: Simplify right side
    82,284x = 32,503,762,944
  5. Step 5: Solve for x
    x = 32,503,762,944/82,284
  6. Step 6: Final answer
    x = 395,019.24

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.