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Finding the Third Proportional to 1,582 and 2,013

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Solution

The third proportional to 1,582 and 2,013 is: 2,561.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,582 : 2,013 = 2,013 : x
  2. Step 2: Convert to fraction form
    1,582/2,013 = 2,013/x
  3. Step 3: Cross multiply
    1,582x = 2,013 × 2,013
  4. Step 4: Simplify right side
    1,582x = 4,052,169
  5. Step 5: Solve for x
    x = 4,052,169/1,582
  6. Step 6: Final answer
    x = 2,561.42

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Why These Related Problems?

These problems maintain the same ratio (1.27) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.