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Finding the Third Proportional to 748 and 1,597

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Solution

The third proportional to 748 and 1,597 is: 3,409.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    748 : 1,597 = 1,597 : x
  2. Step 2: Convert to fraction form
    748/1,597 = 1,597/x
  3. Step 3: Cross multiply
    748x = 1,597 × 1,597
  4. Step 4: Simplify right side
    748x = 2,550,409
  5. Step 5: Solve for x
    x = 2,550,409/748
  6. Step 6: Final answer
    x = 3,409.64

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.