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Finding the Third Proportional to 586.75 and 822.75

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Solution

The third proportional to 586.75 and 822.75 is: 1,153.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    586.75 : 822.75 = 822.75 : x
  2. Step 2: Convert to fraction form
    586.75/822.75 = 822.75/x
  3. Step 3: Cross multiply
    586.75x = 822.75 × 822.75
  4. Step 4: Simplify right side
    586.75x = 676,917.56
  5. Step 5: Solve for x
    x = 676,917.56/586.75
  6. Step 6: Final answer
    x = 1,153.67

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.