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Finding the Fourth Proportional to 823.84, 1,235.76 and 457.72

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Solution

The fourth proportional to 823.84, 1,235.76 and 457.72 is: 686.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    823.84 : 1,235.76 = 457.72 : x
  2. Step 2: Convert to fraction form
    823.84/1,235.76 = 457.72/x
  3. Step 3: Cross multiply
    823.84x = 1,235.76 × 457.72
  4. Step 4: Simplify right side
    823.84x = 565,632.07
  5. Step 5: Solve for x
    x = 565,632.07/823.84
  6. Step 6: Final answer
    x = 686.58

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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.