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Finding the Third Proportional to 409 and 953.50

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Solution

The third proportional to 409 and 953.50 is: 2,222.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 953.50 = 953.50 : x
  2. Step 2: Convert to fraction form
    409/953.50 = 953.50/x
  3. Step 3: Cross multiply
    409x = 953.50 × 953.50
  4. Step 4: Simplify right side
    409x = 909,162.25
  5. Step 5: Solve for x
    x = 909,162.25/409
  6. Step 6: Final answer
    x = 2,222.89

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Why These Related Problems?

These problems maintain the same ratio (2.33) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.