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Finding the Third Proportional to 1,023 and 1,390

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Solution

The third proportional to 1,023 and 1,390 is: 1,888.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,023 : 1,390 = 1,390 : x
  2. Step 2: Convert to fraction form
    1,023/1,390 = 1,390/x
  3. Step 3: Cross multiply
    1,023x = 1,390 × 1,390
  4. Step 4: Simplify right side
    1,023x = 1,932,100
  5. Step 5: Solve for x
    x = 1,932,100/1,023
  6. Step 6: Final answer
    x = 1,888.66

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.