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Finding the Third Proportional to 832 and 1,302

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Solution

The third proportional to 832 and 1,302 is: 2,037.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    832 : 1,302 = 1,302 : x
  2. Step 2: Convert to fraction form
    832/1,302 = 1,302/x
  3. Step 3: Cross multiply
    832x = 1,302 × 1,302
  4. Step 4: Simplify right side
    832x = 1,695,204
  5. Step 5: Solve for x
    x = 1,695,204/832
  6. Step 6: Final answer
    x = 2,037.50

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.