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Finding the Third Proportional to 1,407 and 3,024

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Solution

The third proportional to 1,407 and 3,024 is: 6,499.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,407 : 3,024 = 3,024 : x
  2. Step 2: Convert to fraction form
    1,407/3,024 = 3,024/x
  3. Step 3: Cross multiply
    1,407x = 3,024 × 3,024
  4. Step 4: Simplify right side
    1,407x = 9,144,576
  5. Step 5: Solve for x
    x = 9,144,576/1,407
  6. Step 6: Final answer
    x = 6,499.34

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.