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Finding the Fourth Proportional to 1,057.66, 1,586.14 and 509.50

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Solution

The fourth proportional to 1,057.66, 1,586.14 and 509.50 is: 764.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,057.66 : 1,586.14 = 509.50 : x
  2. Step 2: Convert to fraction form
    1,057.66/1,586.14 = 509.50/x
  3. Step 3: Cross multiply
    1,057.66x = 1,586.14 × 509.50
  4. Step 4: Simplify right side
    1,057.66x = 808,138.33
  5. Step 5: Solve for x
    x = 808,138.33/1,057.66
  6. Step 6: Final answer
    x = 764.08

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.