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Finding the Third Proportional to 7,824 and 12,576

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Solution

The third proportional to 7,824 and 12,576 is: 20,214.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,824 : 12,576 = 12,576 : x
  2. Step 2: Convert to fraction form
    7,824/12,576 = 12,576/x
  3. Step 3: Cross multiply
    7,824x = 12,576 × 12,576
  4. Step 4: Simplify right side
    7,824x = 158,155,776
  5. Step 5: Solve for x
    x = 158,155,776/7,824
  6. Step 6: Final answer
    x = 20,214.18

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.