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Finding the Fourth Proportional to 470, 705.12 and 416

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Solution

The fourth proportional to 470, 705.12 and 416 is: 624.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    470 : 705.12 = 416 : x
  2. Step 2: Convert to fraction form
    470/705.12 = 416/x
  3. Step 3: Cross multiply
    470x = 705.12 × 416
  4. Step 4: Simplify right side
    470x = 293,329.92
  5. Step 5: Solve for x
    x = 293,329.92/470
  6. Step 6: Final answer
    x = 624.11

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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.