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Finding the Third Proportional to 459.84 and 1,023.05

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Solution

The third proportional to 459.84 and 1,023.05 is: 2,276.04

Step by Step Solution

  1. Step 1: Write the proportion equation
    459.84 : 1,023.05 = 1,023.05 : x
  2. Step 2: Convert to fraction form
    459.84/1,023.05 = 1,023.05/x
  3. Step 3: Cross multiply
    459.84x = 1,023.05 × 1,023.05
  4. Step 4: Simplify right side
    459.84x = 1,046,624.91
  5. Step 5: Solve for x
    x = 1,046,624.91/459.84
  6. Step 6: Final answer
    x = 2,276.04

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.