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Finding the Third Proportional to 1,071 and 1,215

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Solution

The third proportional to 1,071 and 1,215 is: 1,378.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,071 : 1,215 = 1,215 : x
  2. Step 2: Convert to fraction form
    1,071/1,215 = 1,215/x
  3. Step 3: Cross multiply
    1,071x = 1,215 × 1,215
  4. Step 4: Simplify right side
    1,071x = 1,476,225
  5. Step 5: Solve for x
    x = 1,476,225/1,071
  6. Step 6: Final answer
    x = 1,378.36

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.