Questions: One number is 3 times another number. If 17 is added to each, the first resulting number is twice the second resulting number. Find the two numbers.

One number is 3 times another number. If 17 is added to each, the first resulting number is twice the second resulting number. Find the two numbers.
Transcript text: One number is 3 times another number. If 17 is added to each, the first resulting number is twice the second resulting number. Find the two numbers.
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Solution

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Solution Steps

Step 1: Define the Variables

Let \( x \) be the first number and \( y \) be the second number.

Step 2: Set Up the Equations

From the problem statement, we have the following equations:

  1. \( x = 3y \) (the first number is 3 times the second number)
  2. \( x + 17 = 2(y + 17) \) (when 17 is added to each, the first is twice the second)
Step 3: Substitute and Simplify

Substituting \( x = 3y \) into the second equation: \[ 3y + 17 = 2(y + 17) \] Expanding the right side: \[ 3y + 17 = 2y + 34 \]

Step 4: Solve for \( y \)

Rearranging the equation gives: \[ 3y - 2y = 34 - 17 \] This simplifies to: \[ y = 17 \]

Step 5: Find \( x \)

Substituting \( y = 17 \) back into the first equation: \[ x = 3y = 3 \times 17 = 51 \]

Step 6: Conclusion

The two numbers are \( x = 51 \) and \( y = 17 \).

Final Answer

The two numbers are \( \boxed{51} \) and \( \boxed{17} \).

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