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Finding the Third Proportional to 824 and 1,830

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Solution

The third proportional to 824 and 1,830 is: 4,064.20

Step by Step Solution

  1. Step 1: Write the proportion equation
    824 : 1,830 = 1,830 : x
  2. Step 2: Convert to fraction form
    824/1,830 = 1,830/x
  3. Step 3: Cross multiply
    824x = 1,830 × 1,830
  4. Step 4: Simplify right side
    824x = 3,348,900
  5. Step 5: Solve for x
    x = 3,348,900/824
  6. Step 6: Final answer
    x = 4,064.20

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Why These Related Problems?

These problems maintain the same ratio (2.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.