Questions: One number is six more than a second number. Twice the first is 6 less than 3 times the second. Find the numbers. Let x represent one number and y represent the second number. Translate the first fact into an equation. Fill in the blanks. In words is six more second than number

Solution Steps

To solve this problem, we need to set up a system of linear equations based on the given conditions and then solve for the variables.

1. Let \( x \) represent the first number and \( y \) represent the second number.
2. According to the problem, the first number is six more than the second number. This translates to the equation: \( x = y + 6 \).
3. The second condition states that twice the first number is six less than three times the second number. This translates to the equation: \( 2x = 3y - 6 \).
4. Solve this system of equations to find the values of \( x \) and \( y \).

Let \( x \) represent the first number and \( y \) represent the second number. According to the problem, we can set up the following equations:

1. \( x = y + 6 \)
2. \( 2x = 3y - 6 \)

We solve the system of equations to find the values of \( x \) and \( y \).

From the first equation: \[ x = y + 6 \]

Substitute \( x \) in the second equation: \[ 2(y + 6) = 3y - 6 \]

Simplify and solve for \( y \): \[ 2y + 12 = 3y - 6 \] \[ 12 + 6 = 3y - 2y \] \[ 18 = y \]

Now, substitute \( y = 18 \) back into the first equation to find \( x \): \[ x = 18 + 6 \] \[ x = 24 \]

Final Answer