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Finding the Third Proportional to 294,142 and 414,213

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Solution

The third proportional to 294,142 and 414,213 is: 583,297.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    294,142 : 414,213 = 414,213 : x
  2. Step 2: Convert to fraction form
    294,142/414,213 = 414,213/x
  3. Step 3: Cross multiply
    294,142x = 414,213 × 414,213
  4. Step 4: Simplify right side
    294,142x = 171,572,409,369
  5. Step 5: Solve for x
    x = 171,572,409,369/294,142
  6. Step 6: Final answer
    x = 583,297.89

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Why These Related Problems?

These problems maintain the same ratio (1.41) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.