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Finding the Third Proportional to 1,457 and 2,082

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Solution

The third proportional to 1,457 and 2,082 is: 2,975.10

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,457 : 2,082 = 2,082 : x
  2. Step 2: Convert to fraction form
    1,457/2,082 = 2,082/x
  3. Step 3: Cross multiply
    1,457x = 2,082 × 2,082
  4. Step 4: Simplify right side
    1,457x = 4,334,724
  5. Step 5: Solve for x
    x = 4,334,724/1,457
  6. Step 6: Final answer
    x = 2,975.10

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.