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Finding the Third Proportional to 5,824 and 6,416

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Solution

The third proportional to 5,824 and 6,416 is: 7,068.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,824 : 6,416 = 6,416 : x
  2. Step 2: Convert to fraction form
    5,824/6,416 = 6,416/x
  3. Step 3: Cross multiply
    5,824x = 6,416 × 6,416
  4. Step 4: Simplify right side
    5,824x = 41,165,056
  5. Step 5: Solve for x
    x = 41,165,056/5,824
  6. Step 6: Final answer
    x = 7,068.18

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.