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Finding the Third Proportional to 1,023 and 2,265

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Solution

The third proportional to 1,023 and 2,265 is: 5,014.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023 : 2,265 = 2,265 : x
  2. Step 2: Convert to fraction form
    1,023/2,265 = 2,265/x
  3. Step 3: Cross multiply
    1,023x = 2,265 × 2,265
  4. Step 4: Simplify right side
    1,023x = 5,130,225
  5. Step 5: Solve for x
    x = 5,130,225/1,023
  6. Step 6: Final answer
    x = 5,014.88

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.