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Finding the Fourth Proportional to 762.45, 1,052.19 and 413.14

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Solution

The fourth proportional to 762.45, 1,052.19 and 413.14 is: 570.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    762.45 : 1,052.19 = 413.14 : x
  2. Step 2: Convert to fraction form
    762.45/1,052.19 = 413.14/x
  3. Step 3: Cross multiply
    762.45x = 1,052.19 × 413.14
  4. Step 4: Simplify right side
    762.45x = 434,698.16
  5. Step 5: Solve for x
    x = 434,698.16/762.45
  6. Step 6: Final answer
    x = 570.13

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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.