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Finding the Third Proportional to 83,200 and 180,224

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Solution

The third proportional to 83,200 and 180,224 is: 390,392.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,200 : 180,224 = 180,224 : x
  2. Step 2: Convert to fraction form
    83,200/180,224 = 180,224/x
  3. Step 3: Cross multiply
    83,200x = 180,224 × 180,224
  4. Step 4: Simplify right side
    83,200x = 32,480,690,176
  5. Step 5: Solve for x
    x = 32,480,690,176/83,200
  6. Step 6: Final answer
    x = 390,392.91

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.