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Finding the Third Proportional to 898 and 1,409.50

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Solution

The third proportional to 898 and 1,409.50 is: 2,212.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    898 : 1,409.50 = 1,409.50 : x
  2. Step 2: Convert to fraction form
    898/1,409.50 = 1,409.50/x
  3. Step 3: Cross multiply
    898x = 1,409.50 × 1,409.50
  4. Step 4: Simplify right side
    898x = 1,986,690.25
  5. Step 5: Solve for x
    x = 1,986,690.25/898
  6. Step 6: Final answer
    x = 2,212.35

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.