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Finding the Fourth Proportional to 1,057.34, 1,585.76 and 509.24

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Solution

The fourth proportional to 1,057.34, 1,585.76 and 509.24 is: 763.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,057.34 : 1,585.76 = 509.24 : x
  2. Step 2: Convert to fraction form
    1,057.34/1,585.76 = 509.24/x
  3. Step 3: Cross multiply
    1,057.34x = 1,585.76 × 509.24
  4. Step 4: Simplify right side
    1,057.34x = 807,532.42
  5. Step 5: Solve for x
    x = 807,532.42/1,057.34
  6. Step 6: Final answer
    x = 763.74

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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.