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Finding the Fourth Proportional to 971.68, 1,457.40 and 509.20

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Solution

The fourth proportional to 971.68, 1,457.40 and 509.20 is: 763.74

Step by Step Solution

  1. Step 1: Write the proportion equation
    971.68 : 1,457.40 = 509.20 : x
  2. Step 2: Convert to fraction form
    971.68/1,457.40 = 509.20/x
  3. Step 3: Cross multiply
    971.68x = 1,457.40 × 509.20
  4. Step 4: Simplify right side
    971.68x = 742,108.08
  5. Step 5: Solve for x
    x = 742,108.08/971.68
  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.