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Finding the Third Proportional to 1,565 and 3,409

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Solution

The third proportional to 1,565 and 3,409 is: 7,425.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,565 : 3,409 = 3,409 : x
  2. Step 2: Convert to fraction form
    1,565/3,409 = 3,409/x
  3. Step 3: Cross multiply
    1,565x = 3,409 × 3,409
  4. Step 4: Simplify right side
    1,565x = 11,621,281
  5. Step 5: Solve for x
    x = 11,621,281/1,565
  6. Step 6: Final answer
    x = 7,425.74

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.