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Finding the Third Proportional to 314.75 and 459.50

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Solution

The third proportional to 314.75 and 459.50 is: 670.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.75 : 459.50 = 459.50 : x
  2. Step 2: Convert to fraction form
    314.75/459.50 = 459.50/x
  3. Step 3: Cross multiply
    314.75x = 459.50 × 459.50
  4. Step 4: Simplify right side
    314.75x = 211,140.25
  5. Step 5: Solve for x
    x = 211,140.25/314.75
  6. Step 6: Final answer
    x = 670.82

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.