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Finding the Fourth Proportional to 971.48, 1,457.42 and 509.78

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Solution

The fourth proportional to 971.48, 1,457.42 and 509.78 is: 764.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    971.48 : 1,457.42 = 509.78 : x
  2. Step 2: Convert to fraction form
    971.48/1,457.42 = 509.78/x
  3. Step 3: Cross multiply
    971.48x = 1,457.42 × 509.78
  4. Step 4: Simplify right side
    971.48x = 742,953.73
  5. Step 5: Solve for x
    x = 742,953.73/971.48
  6. Step 6: Final answer
    x = 764.77

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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.