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Finding the Third Proportional to 830 and 1,214

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Solution

The third proportional to 830 and 1,214 is: 1,775.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    830 : 1,214 = 1,214 : x
  2. Step 2: Convert to fraction form
    830/1,214 = 1,214/x
  3. Step 3: Cross multiply
    830x = 1,214 × 1,214
  4. Step 4: Simplify right side
    830x = 1,473,796
  5. Step 5: Solve for x
    x = 1,473,796/830
  6. Step 6: Final answer
    x = 1,775.66

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.