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Finding the Third Proportional to 1,650 and 2,409

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Solution

The third proportional to 1,650 and 2,409 is: 3,517.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,650 : 2,409 = 2,409 : x
  2. Step 2: Convert to fraction form
    1,650/2,409 = 2,409/x
  3. Step 3: Cross multiply
    1,650x = 2,409 × 2,409
  4. Step 4: Simplify right side
    1,650x = 5,803,281
  5. Step 5: Solve for x
    x = 5,803,281/1,650
  6. Step 6: Final answer
    x = 3,517.14

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Why These Related Problems?

These problems maintain the same ratio (1.46) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.