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Finding the Fourth Proportional to 1,411.64, 1,948.19 and 782.24

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Solution

The fourth proportional to 1,411.64, 1,948.19 and 782.24 is: 1,079.55

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,411.64 : 1,948.19 = 782.24 : x
  2. Step 2: Convert to fraction form
    1,411.64/1,948.19 = 782.24/x
  3. Step 3: Cross multiply
    1,411.64x = 1,948.19 × 782.24
  4. Step 4: Simplify right side
    1,411.64x = 1,523,938.49
  5. Step 5: Solve for x
    x = 1,523,938.49/1,411.64
  6. Step 6: Final answer
    x = 1,079.55

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.