Martha just started a new job as an engineer. she is given a $9,000 sign on bonus and paid $4,500 per month . write and solve an equation to determine the number of months that martha must work before she earns $27,000

$27,000=$4,500X+$9,000
-$9000=$4500X
$18,000=$4500X
\$4500=\4500
4=x

She needs to work for 4 months

Imagine that x is the number of months that Martha has worked before earning 27,000 dollars. We also know that since the $9,000 is also included in the earning of $27,000, we will be adding $9,000 to however the rest of the equation. Since she earns $4,500 per month, and she works for x months, we can multiply these two together to form the money earned (without bonuses) after x months, 4,500x. Now we can make our equation.

$9,000 + 4,500x =$27,000
4,500x = $18,000                               Subtract $9,000 to get x on one side
x = 4 months                                     Divide by 4,500 to get x by itself