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Finding the Third Proportional to 1,106 and 1,586

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Solution

The third proportional to 1,106 and 1,586 is: 2,274.32

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,106 : 1,586 = 1,586 : x
  2. Step 2: Convert to fraction form
    1,106/1,586 = 1,586/x
  3. Step 3: Cross multiply
    1,106x = 1,586 × 1,586
  4. Step 4: Simplify right side
    1,106x = 2,515,396
  5. Step 5: Solve for x
    x = 2,515,396/1,106
  6. Step 6: Final answer
    x = 2,274.32

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.