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Finding the Third Proportional to 1,102 and 1,302

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Solution

The third proportional to 1,102 and 1,302 is: 1,538.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,102 : 1,302 = 1,302 : x
  2. Step 2: Convert to fraction form
    1,102/1,302 = 1,302/x
  3. Step 3: Cross multiply
    1,102x = 1,302 × 1,302
  4. Step 4: Simplify right side
    1,102x = 1,695,204
  5. Step 5: Solve for x
    x = 1,695,204/1,102
  6. Step 6: Final answer
    x = 1,538.30

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.