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Finding the Third Proportional to 1,205 and 1,309

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Solution

The third proportional to 1,205 and 1,309 is: 1,421.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,205 : 1,309 = 1,309 : x
  2. Step 2: Convert to fraction form
    1,205/1,309 = 1,309/x
  3. Step 3: Cross multiply
    1,205x = 1,309 × 1,309
  4. Step 4: Simplify right side
    1,205x = 1,713,481
  5. Step 5: Solve for x
    x = 1,713,481/1,205
  6. Step 6: Final answer
    x = 1,421.98

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.