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Finding the Third Proportional to 1,582 and 2,419

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Solution

The third proportional to 1,582 and 2,419 is: 3,698.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,582 : 2,419 = 2,419 : x
  2. Step 2: Convert to fraction form
    1,582/2,419 = 2,419/x
  3. Step 3: Cross multiply
    1,582x = 2,419 × 2,419
  4. Step 4: Simplify right side
    1,582x = 5,851,561
  5. Step 5: Solve for x
    x = 5,851,561/1,582
  6. Step 6: Final answer
    x = 3,698.84

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.