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Finding the Third Proportional to 7,824 and 15,840

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Solution

The third proportional to 7,824 and 15,840 is: 32,068.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,824 : 15,840 = 15,840 : x
  2. Step 2: Convert to fraction form
    7,824/15,840 = 15,840/x
  3. Step 3: Cross multiply
    7,824x = 15,840 × 15,840
  4. Step 4: Simplify right side
    7,824x = 250,905,600
  5. Step 5: Solve for x
    x = 250,905,600/7,824
  6. Step 6: Final answer
    x = 32,068.71

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.