Questions: Translate the second fact into an equation. Fill in the blanks.

Solution Steps

• The first fact states: "One number is six more than a second number."
• Let $x$ be the first number and $y$ be the second number.
• This translates to: $x = y + 6$.

• The second fact states: "Twice the first number is 6 less than 3 times the second number."
• This translates to: $2x = 3y - 6$.

• We have two equations:

  1. $x = y + 6$
  2. $2x = 3y - 6$

• Substitute $x = y + 6$ into $2x = 3y - 6$: $$2(y + 6) = 3y - 6$$ $$2y + 12 = 3y - 6$$ $$12 + 6 = 3y - 2y$$ $$18 = y$$

• Substitute $y = 18$ back into $x = y + 6$: $$x = 18 + 6$$ $$x = 24$$

Final Answer