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Finding the Third Proportional to 1,214 and 1,403

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Solution

The third proportional to 1,214 and 1,403 is: 1,621.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,214 : 1,403 = 1,403 : x
  2. Step 2: Convert to fraction form
    1,214/1,403 = 1,403/x
  3. Step 3: Cross multiply
    1,214x = 1,403 × 1,403
  4. Step 4: Simplify right side
    1,214x = 1,968,409
  5. Step 5: Solve for x
    x = 1,968,409/1,214
  6. Step 6: Final answer
    x = 1,621.42

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.