Find the unknown numbers.
One number is nine less than another. Their sum is negative twenty-seven.

• A. $-18$ and $-27$
• B. $-18$ and $-9$
• C. $-27$ and $-9$
• D. $-9$ and $18$

Answer: (B)

Verified step by step guidance

1. Let the two unknown numbers be represented as variables. For example, let the first number be \(x\) and the second number be \(y\).
2. Translate the first statement "One number is nine less than another" into an equation. This can be written as \(x = y - 9\) or \(y = x + 9\) depending on which number you assign as \(x\) or \(y\).
3. Translate the second statement "Their sum is negative twenty-seven" into an equation: \(x + y = -27\).
4. Substitute the expression from the first equation into the second equation to have one equation with one variable. For example, if \(x = y - 9\), substitute into \(x + y = -27\) to get \((y - 9) + y = -27\).
5. Solve the resulting equation for the single variable, then use that value to find the other number by substituting back into the first equation.