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Finding the Third Proportional to 305.69 and 459.98

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Solution

The third proportional to 305.69 and 459.98 is: 692.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    305.69 : 459.98 = 459.98 : x
  2. Step 2: Convert to fraction form
    305.69/459.98 = 459.98/x
  3. Step 3: Cross multiply
    305.69x = 459.98 × 459.98
  4. Step 4: Simplify right side
    305.69x = 211,585.63
  5. Step 5: Solve for x
    x = 211,585.63/305.69
  6. Step 6: Final answer
    x = 692.16

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.