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Finding the Third Proportional to 977 and 2,534

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Solution

The third proportional to 977 and 2,534 is: 6,572.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    977 : 2,534 = 2,534 : x
  2. Step 2: Convert to fraction form
    977/2,534 = 2,534/x
  3. Step 3: Cross multiply
    977x = 2,534 × 2,534
  4. Step 4: Simplify right side
    977x = 6,421,156
  5. Step 5: Solve for x
    x = 6,421,156/977
  6. Step 6: Final answer
    x = 6,572.32

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Why These Related Problems?

These problems maintain the same ratio (2.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.