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Finding the Fourth Proportional to 507.40, 699.86 and 409

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Solution

The fourth proportional to 507.40, 699.86 and 409 is: 564.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    507.40 : 699.86 = 409 : x
  2. Step 2: Convert to fraction form
    507.40/699.86 = 409/x
  3. Step 3: Cross multiply
    507.40x = 699.86 × 409
  4. Step 4: Simplify right side
    507.40x = 286,242.74
  5. Step 5: Solve for x
    x = 286,242.74/507.40
  6. Step 6: Final answer
    x = 564.14

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.