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Finding the Third Proportional to 1,565 and 2,369

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Solution

The third proportional to 1,565 and 2,369 is: 3,586.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,565 : 2,369 = 2,369 : x
  2. Step 2: Convert to fraction form
    1,565/2,369 = 2,369/x
  3. Step 3: Cross multiply
    1,565x = 2,369 × 2,369
  4. Step 4: Simplify right side
    1,565x = 5,612,161
  5. Step 5: Solve for x
    x = 5,612,161/1,565
  6. Step 6: Final answer
    x = 3,586.05

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.