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Finding the Third Proportional to 542 and 1,409

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Solution

The third proportional to 542 and 1,409 is: 3,662.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    542 : 1,409 = 1,409 : x
  2. Step 2: Convert to fraction form
    542/1,409 = 1,409/x
  3. Step 3: Cross multiply
    542x = 1,409 × 1,409
  4. Step 4: Simplify right side
    542x = 1,985,281
  5. Step 5: Solve for x
    x = 1,985,281/542
  6. Step 6: Final answer
    x = 3,662.88

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Why These Related Problems?

These problems maintain the same ratio (2.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.