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Finding the Third Proportional to 2,565 and 3,424

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Solution

The third proportional to 2,565 and 3,424 is: 4,570.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,565 : 3,424 = 3,424 : x
  2. Step 2: Convert to fraction form
    2,565/3,424 = 3,424/x
  3. Step 3: Cross multiply
    2,565x = 3,424 × 3,424
  4. Step 4: Simplify right side
    2,565x = 11,723,776
  5. Step 5: Solve for x
    x = 11,723,776/2,565
  6. Step 6: Final answer
    x = 4,570.67

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Why These Related Problems?

These problems maintain the same ratio (1.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.