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Finding the Third Proportional to 977 and 1,509

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Solution

The third proportional to 977 and 1,509 is: 2,330.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 1,509 = 1,509 : x
  2. Step 2: Convert to fraction form
    977/1,509 = 1,509/x
  3. Step 3: Cross multiply
    977x = 1,509 × 1,509
  4. Step 4: Simplify right side
    977x = 2,277,081
  5. Step 5: Solve for x
    x = 2,277,081/977
  6. Step 6: Final answer
    x = 2,330.69

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.