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Finding the Third Proportional to 716 and 1,565

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Solution

The third proportional to 716 and 1,565 is: 3,420.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    716 : 1,565 = 1,565 : x
  2. Step 2: Convert to fraction form
    716/1,565 = 1,565/x
  3. Step 3: Cross multiply
    716x = 1,565 × 1,565
  4. Step 4: Simplify right side
    716x = 2,449,225
  5. Step 5: Solve for x
    x = 2,449,225/716
  6. Step 6: Final answer
    x = 3,420.71

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.