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Finding the Third Proportional to 208,085 and 314,316

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Solution

The third proportional to 208,085 and 314,316 is: 474,779.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    208,085 : 314,316 = 314,316 : x
  2. Step 2: Convert to fraction form
    208,085/314,316 = 314,316/x
  3. Step 3: Cross multiply
    208,085x = 314,316 × 314,316
  4. Step 4: Simplify right side
    208,085x = 98,794,547,856
  5. Step 5: Solve for x
    x = 98,794,547,856/208,085
  6. Step 6: Final answer
    x = 474,779.77

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.