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Finding the Third Proportional to 1,409.50 and 1,567

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Solution

The third proportional to 1,409.50 and 1,567 is: 1,742.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,409.50 : 1,567 = 1,567 : x
  2. Step 2: Convert to fraction form
    1,409.50/1,567 = 1,567/x
  3. Step 3: Cross multiply
    1,409.50x = 1,567 × 1,567
  4. Step 4: Simplify right side
    1,409.50x = 2,455,489
  5. Step 5: Solve for x
    x = 2,455,489/1,409.50
  6. Step 6: Final answer
    x = 1,742.10

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.