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Finding the Third Proportional to 976 and 1,586

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Solution

The third proportional to 976 and 1,586 is: 2,577.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    976 : 1,586 = 1,586 : x
  2. Step 2: Convert to fraction form
    976/1,586 = 1,586/x
  3. Step 3: Cross multiply
    976x = 1,586 × 1,586
  4. Step 4: Simplify right side
    976x = 2,515,396
  5. Step 5: Solve for x
    x = 2,515,396/976
  6. Step 6: Final answer
    x = 2,577.25

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.