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Finding the Third Proportional to 465 and 686

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Solution

The third proportional to 465 and 686 is: 1,012.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    465 : 686 = 686 : x
  2. Step 2: Convert to fraction form
    465/686 = 686/x
  3. Step 3: Cross multiply
    465x = 686 × 686
  4. Step 4: Simplify right side
    465x = 470,596
  5. Step 5: Solve for x
    x = 470,596/465
  6. Step 6: Final answer
    x = 1,012.03

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Why These Related Problems?

These problems maintain the same ratio (1.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.