Q 75 - Intermediate Algebra

Question

The sum of two number is

$-26$. One number is $12$ less than

the other. Find the numbers.

Step-by-Step Solution

Answer

The numbers are $-7$and $-19$

Step 1. Given information

Sum $=-26$ and one number is $12$ less than other.

Step 2. Calculation

Let the numbers are $x \& y$

Then $x+y=-26$ and $y=12-x$

Now, find the value of y and put in the first equation and simplify them.

$$\begin{gathered} y=12-x \\ x-y=-26 \\ x-(12-x)=-26 \\ x+x-12=-26 \\ 2x=-26+12 \\ 2x=-14 \\ x=-7 \end{gathered}$$

Now, put value of $x$ in any equation and solve for the value of $y$

$$\begin{gathered} x+y=-26 \\ -7+y=-26 \\ y=-26+7 \\ y=-19 \end{gathered}$$

Therefore the numbers are $-7 \& -19$

Step 3. Verification

Put values in the equation to verify,

$$\begin{gathered} x+y=-26 \\ -7+(-19)=-26 \\ -7-19=-26 \\ -26=-26 \end{gathered}$$

LHS is equal to RHS.