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Finding the Third Proportional to 5,994 and 7,830

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Solution

The third proportional to 5,994 and 7,830 is: 10,228.38

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,994 : 7,830 = 7,830 : x
  2. Step 2: Convert to fraction form
    5,994/7,830 = 7,830/x
  3. Step 3: Cross multiply
    5,994x = 7,830 × 7,830
  4. Step 4: Simplify right side
    5,994x = 61,308,900
  5. Step 5: Solve for x
    x = 61,308,900/5,994
  6. Step 6: Final answer
    x = 10,228.38

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.