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Finding the Third Proportional to 1,564 and 3,416

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Solution

The third proportional to 1,564 and 3,416 is: 7,461.03

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,564 : 3,416 = 3,416 : x
  2. Step 2: Convert to fraction form
    1,564/3,416 = 3,416/x
  3. Step 3: Cross multiply
    1,564x = 3,416 × 3,416
  4. Step 4: Simplify right side
    1,564x = 11,669,056
  5. Step 5: Solve for x
    x = 11,669,056/1,564
  6. Step 6: Final answer
    x = 7,461.03

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.