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Finding the Third Proportional to 1,582 and 4,078

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Solution

The third proportional to 1,582 and 4,078 is: 10,512.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,582 : 4,078 = 4,078 : x
  2. Step 2: Convert to fraction form
    1,582/4,078 = 4,078/x
  3. Step 3: Cross multiply
    1,582x = 4,078 × 4,078
  4. Step 4: Simplify right side
    1,582x = 16,630,084
  5. Step 5: Solve for x
    x = 16,630,084/1,582
  6. Step 6: Final answer
    x = 10,512.06

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Why These Related Problems?

These problems maintain the same ratio (2.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.