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Finding the Third Proportional to 970 and 2,065

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Solution

The third proportional to 970 and 2,065 is: 4,396.11

Step by Step Solution

  1. Step 1: Write the proportion equation
    970 : 2,065 = 2,065 : x
  2. Step 2: Convert to fraction form
    970/2,065 = 2,065/x
  3. Step 3: Cross multiply
    970x = 2,065 × 2,065
  4. Step 4: Simplify right side
    970x = 4,264,225
  5. Step 5: Solve for x
    x = 4,264,225/970
  6. Step 6: Final answer
    x = 4,396.11

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.