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Finding the Third Proportional to 977 and 1,523

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Solution

The third proportional to 977 and 1,523 is: 2,374.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,523 = 1,523 : x
  2. Step 2: Convert to fraction form
    977/1,523 = 1,523/x
  3. Step 3: Cross multiply
    977x = 1,523 × 1,523
  4. Step 4: Simplify right side
    977x = 2,319,529
  5. Step 5: Solve for x
    x = 2,319,529/977
  6. Step 6: Final answer
    x = 2,374.13

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.