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Finding the Third Proportional to 1,407 and 2,102.63

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Solution

The third proportional to 1,407 and 2,102.63 is: 3,142.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407 : 2,102.63 = 2,102.63 : x
  2. Step 2: Convert to fraction form
    1,407/2,102.63 = 2,102.63/x
  3. Step 3: Cross multiply
    1,407x = 2,102.63 × 2,102.63
  4. Step 4: Simplify right side
    1,407x = 4,421,031.89
  5. Step 5: Solve for x
    x = 4,421,031.89/1,407
  6. Step 6: Final answer
    x = 3,142.17

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.