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Finding the Third Proportional to 523 and 784

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Solution

The third proportional to 523 and 784 is: 1,175.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    523 : 784 = 784 : x
  2. Step 2: Convert to fraction form
    523/784 = 784/x
  3. Step 3: Cross multiply
    523x = 784 × 784
  4. Step 4: Simplify right side
    523x = 614,656
  5. Step 5: Solve for x
    x = 614,656/523
  6. Step 6: Final answer
    x = 1,175.25

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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.