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Finding the Fourth Proportional to 784, 1,176 and 442

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Solution

The fourth proportional to 784, 1,176 and 442 is: 663

Step by Step Solution

  1. Step 1: Write the proportion equation
    784 : 1,176 = 442 : x
  2. Step 2: Convert to fraction form
    784/1,176 = 442/x
  3. Step 3: Cross multiply
    784x = 1,176 × 442
  4. Step 4: Simplify right side
    784x = 519,792
  5. Step 5: Solve for x
    x = 519,792/784
  6. Step 6: Final answer
    x = 663

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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.