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Finding the Third Proportional to 6,574 and 7,214

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Solution

The third proportional to 6,574 and 7,214 is: 7,916.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,574 : 7,214 = 7,214 : x
  2. Step 2: Convert to fraction form
    6,574/7,214 = 7,214/x
  3. Step 3: Cross multiply
    6,574x = 7,214 × 7,214
  4. Step 4: Simplify right side
    6,574x = 52,041,796
  5. Step 5: Solve for x
    x = 52,041,796/6,574
  6. Step 6: Final answer
    x = 7,916.31

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.