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Finding the Third Proportional to 314.50 and 686.75

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Solution

The third proportional to 314.50 and 686.75 is: 1,499.60

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.50 : 686.75 = 686.75 : x
  2. Step 2: Convert to fraction form
    314.50/686.75 = 686.75/x
  3. Step 3: Cross multiply
    314.50x = 686.75 × 686.75
  4. Step 4: Simplify right side
    314.50x = 471,625.56
  5. Step 5: Solve for x
    x = 471,625.56/314.50
  6. Step 6: Final answer
    x = 1,499.60

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.