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Finding the Third Proportional to 2,142 and 3,420

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Solution

The third proportional to 2,142 and 3,420 is: 5,460.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,142 : 3,420 = 3,420 : x
  2. Step 2: Convert to fraction form
    2,142/3,420 = 3,420/x
  3. Step 3: Cross multiply
    2,142x = 3,420 × 3,420
  4. Step 4: Simplify right side
    2,142x = 11,696,400
  5. Step 5: Solve for x
    x = 11,696,400/2,142
  6. Step 6: Final answer
    x = 5,460.50

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.