Question

The sum of two numbers is negative nine. One number is 9 more than another number. What isthe larger number?OnlinententReview the Linked Section of the Prealgebra Textbook for Problem Helpok

Answer 1

The larger number is 0 (zero)

Step-by-step explanation:

We start off by representing the unknown numbers with variables

Let the larger number be x while the smaller one is y

The sum of the two numbers is -9

`x\text{ + y = -9}`

The smaller number is 9 less than the larger number:

`\begin{gathered} x-y\text{ = 9} \\ x\text{ = 9 + y} \end{gathered}`

Now, insert the second equation into the first

Mathematically, we have this as:

`\begin{gathered} 9\text{ + y + y= -9} \\ 2y\text{ = -9-9} \\ 2y\text{ = -18} \\ y\text{ = }(-18)/(2) \\ y\text{ = -9} \end{gathered}`

Recall:

`\begin{gathered} x\text{ = 9 + y} \\ \text{ = 9 + (-9) = 0} \end{gathered}`

0 is greater than -9 and thus, it is the larger number