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 choose to express in terms of the other.
3. Translate the second statement "Their sum is negative twenty-seven" into an equation: \(x + y = -27\).
4. Substitute the expression from step 2 (for example, \(x = y - 9\)) into the sum equation from step 3 to get an equation with one variable: \((y - 9) + y = -27\).
5. Simplify the equation from step 4 and solve for the variable \(y\). Once you find \(y\), substitute it back into the expression from step 2 to find \(x\).