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Finding the Third Proportional to 1,165 and 2,465

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Solution

The third proportional to 1,165 and 2,465 is: 5,215.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,165 : 2,465 = 2,465 : x
  2. Step 2: Convert to fraction form
    1,165/2,465 = 2,465/x
  3. Step 3: Cross multiply
    1,165x = 2,465 × 2,465
  4. Step 4: Simplify right side
    1,165x = 6,076,225
  5. Step 5: Solve for x
    x = 6,076,225/1,165
  6. Step 6: Final answer
    x = 5,215.64

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.