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Finding the Third Proportional to 7,827 and 14,070

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Solution

The third proportional to 7,827 and 14,070 is: 25,292.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,827 : 14,070 = 14,070 : x
  2. Step 2: Convert to fraction form
    7,827/14,070 = 14,070/x
  3. Step 3: Cross multiply
    7,827x = 14,070 × 14,070
  4. Step 4: Simplify right side
    7,827x = 197,964,900
  5. Step 5: Solve for x
    x = 197,964,900/7,827
  6. Step 6: Final answer
    x = 25,292.56

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Why These Related Problems?

These problems maintain the same ratio (1.80) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.