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Finding the Third Proportional to 1,216 and 1,315

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Solution

The third proportional to 1,216 and 1,315 is: 1,422.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,216 : 1,315 = 1,315 : x
  2. Step 2: Convert to fraction form
    1,216/1,315 = 1,315/x
  3. Step 3: Cross multiply
    1,216x = 1,315 × 1,315
  4. Step 4: Simplify right side
    1,216x = 1,729,225
  5. Step 5: Solve for x
    x = 1,729,225/1,216
  6. Step 6: Final answer
    x = 1,422.06

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.