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Finding the Third Proportional to 1,440 and 2,042

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Solution

The third proportional to 1,440 and 2,042 is: 2,895.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,440 : 2,042 = 2,042 : x
  2. Step 2: Convert to fraction form
    1,440/2,042 = 2,042/x
  3. Step 3: Cross multiply
    1,440x = 2,042 × 2,042
  4. Step 4: Simplify right side
    1,440x = 4,169,764
  5. Step 5: Solve for x
    x = 4,169,764/1,440
  6. Step 6: Final answer
    x = 2,895.67

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.