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Finding the Fourth Proportional to 1,057.10, 1,586.59 and 509.47

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Solution

The fourth proportional to 1,057.10, 1,586.59 and 509.47 is: 764.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,057.10 : 1,586.59 = 509.47 : x
  2. Step 2: Convert to fraction form
    1,057.10/1,586.59 = 509.47/x
  3. Step 3: Cross multiply
    1,057.10x = 1,586.59 × 509.47
  4. Step 4: Simplify right side
    1,057.10x = 808,314.77
  5. Step 5: Solve for x
    x = 808,314.77/1,057.10
  6. Step 6: Final answer
    x = 764.66

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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.