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