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Finding the Third Proportional to 465 and 596.50

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Solution

The third proportional to 465 and 596.50 is: 765.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    465 : 596.50 = 596.50 : x
  2. Step 2: Convert to fraction form
    465/596.50 = 596.50/x
  3. Step 3: Cross multiply
    465x = 596.50 × 596.50
  4. Step 4: Simplify right side
    465x = 355,812.25
  5. Step 5: Solve for x
    x = 355,812.25/465
  6. Step 6: Final answer
    x = 765.19

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Why These Related Problems?

These problems maintain the same ratio (1.28) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.