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Finding the Third Proportional to 514 and 829.50

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Solution

The third proportional to 514 and 829.50 is: 1,338.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    514 : 829.50 = 829.50 : x
  2. Step 2: Convert to fraction form
    514/829.50 = 829.50/x
  3. Step 3: Cross multiply
    514x = 829.50 × 829.50
  4. Step 4: Simplify right side
    514x = 688,070.25
  5. Step 5: Solve for x
    x = 688,070.25/514
  6. Step 6: Final answer
    x = 1,338.66

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.