Question

The sum of two numbers is negative eighteen. One number is forty more than the other. Find the numbers.

Short answer

$11$and$(-29)$are the numbers.

Step-by-step solution

Step 1. Assume the numbers

Let the numbers are $\text{'}a\text{'}$and$\text{'}b\text{'}$.

Step 2. Form the first equation.

Since, "Sum of two numbers is$-18$"

Equation for the statement will be,

$a+b=-18$

$b=-18-a$

Step 3. Form the second equation.

Second statement is, "One number is $40$more than the other".

$a=b+40$

Step 4. Substitute the value of 'a' and'b',

$a=(-18-a)+40$

$a=-a+22$

$a+a=-a+22+a$

$2a=22$

Step 5. Divide both the sides of the equation by 2,

$\frac{2a}{2}=\frac{22}{2}$

$a=11$

Step 6. Substitute the value of a to get the numbers.

$a=11$

role="math" localid="1644182850259" $b=-18-11$

$b=-29$