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Finding the Third Proportional to 401,196 and 589,509

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Solution

The third proportional to 401,196 and 589,509 is: 866,212.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    401,196 : 589,509 = 589,509 : x
  2. Step 2: Convert to fraction form
    401,196/589,509 = 589,509/x
  3. Step 3: Cross multiply
    401,196x = 589,509 × 589,509
  4. Step 4: Simplify right side
    401,196x = 347,520,861,081
  5. Step 5: Solve for x
    x = 347,520,861,081/401,196
  6. Step 6: Final answer
    x = 866,212.18

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.