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Finding the Third Proportional to 459.84 and 690.19

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Solution

The third proportional to 459.84 and 690.19 is: 1,035.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    459.84 : 690.19 = 690.19 : x
  2. Step 2: Convert to fraction form
    459.84/690.19 = 690.19/x
  3. Step 3: Cross multiply
    459.84x = 690.19 × 690.19
  4. Step 4: Simplify right side
    459.84x = 476,358.79
  5. Step 5: Solve for x
    x = 476,358.79/459.84
  6. Step 6: Final answer
    x = 1,035.91

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