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Finding the Third Proportional to 1,596 and 1,724

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Solution

The third proportional to 1,596 and 1,724 is: 1,862.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,596 : 1,724 = 1,724 : x
  2. Step 2: Convert to fraction form
    1,596/1,724 = 1,724/x
  3. Step 3: Cross multiply
    1,596x = 1,724 × 1,724
  4. Step 4: Simplify right side
    1,596x = 2,972,176
  5. Step 5: Solve for x
    x = 2,972,176/1,596
  6. Step 6: Final answer
    x = 1,862.27

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.