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Finding the Third Proportional to 1,274 and 1,382

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Solution

The third proportional to 1,274 and 1,382 is: 1,499.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,274 : 1,382 = 1,382 : x
  2. Step 2: Convert to fraction form
    1,274/1,382 = 1,382/x
  3. Step 3: Cross multiply
    1,274x = 1,382 × 1,382
  4. Step 4: Simplify right side
    1,274x = 1,909,924
  5. Step 5: Solve for x
    x = 1,909,924/1,274
  6. Step 6: Final answer
    x = 1,499.16

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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.