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Finding the Fourth Proportional to 1,406.51, 2,109.90 and 419.31

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Solution

The fourth proportional to 1,406.51, 2,109.90 and 419.31 is: 629.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,406.51 : 2,109.90 = 419.31 : x
  2. Step 2: Convert to fraction form
    1,406.51/2,109.90 = 419.31/x
  3. Step 3: Cross multiply
    1,406.51x = 2,109.90 × 419.31
  4. Step 4: Simplify right side
    1,406.51x = 884,701.38
  5. Step 5: Solve for x
    x = 884,701.38/1,406.51
  6. Step 6: Final answer
    x = 629.00

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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.