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Finding the Fourth Proportional to 1,057.46, 1,586.52 and 509.67

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Solution

The fourth proportional to 1,057.46, 1,586.52 and 509.67 is: 764.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,057.46 : 1,586.52 = 509.67 : x
  2. Step 2: Convert to fraction form
    1,057.46/1,586.52 = 509.67/x
  3. Step 3: Cross multiply
    1,057.46x = 1,586.52 × 509.67
  4. Step 4: Simplify right side
    1,057.46x = 808,601.65
  5. Step 5: Solve for x
    x = 808,601.65/1,057.46
  6. Step 6: Final answer
    x = 764.67

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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.