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Finding the Third Proportional to 2,970 and 6,507

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Solution

The third proportional to 2,970 and 6,507 is: 14,256.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,970 : 6,507 = 6,507 : x
  2. Step 2: Convert to fraction form
    2,970/6,507 = 6,507/x
  3. Step 3: Cross multiply
    2,970x = 6,507 × 6,507
  4. Step 4: Simplify right side
    2,970x = 42,341,049
  5. Step 5: Solve for x
    x = 42,341,049/2,970
  6. Step 6: Final answer
    x = 14,256.25

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.