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Finding the Third Proportional to 1,430 and 3,184

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Solution

The third proportional to 1,430 and 3,184 is: 7,089.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,430 : 3,184 = 3,184 : x
  2. Step 2: Convert to fraction form
    1,430/3,184 = 3,184/x
  3. Step 3: Cross multiply
    1,430x = 3,184 × 3,184
  4. Step 4: Simplify right side
    1,430x = 10,137,856
  5. Step 5: Solve for x
    x = 10,137,856/1,430
  6. Step 6: Final answer
    x = 7,089.41

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Why These Related Problems?

These problems maintain the same ratio (2.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.