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Finding the Third Proportional to 824.50 and 1,277

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Solution

The third proportional to 824.50 and 1,277 is: 1,977.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    824.50 : 1,277 = 1,277 : x
  2. Step 2: Convert to fraction form
    824.50/1,277 = 1,277/x
  3. Step 3: Cross multiply
    824.50x = 1,277 × 1,277
  4. Step 4: Simplify right side
    824.50x = 1,630,729
  5. Step 5: Solve for x
    x = 1,630,729/824.50
  6. Step 6: Final answer
    x = 1,977.84

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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.