The width and the length of a rectangle are consecutive even integers. if the width is decreased by 3 inches, then the area of the resulting rectangle is 24 square inches. what is the area of the original rectangle?

12 square inches
48 square inches
96 square inches

Greetings!

To solve this problem, we will have to create a linear system:

Let Statements:
Let x represent the width of the first rectangle
Let y represent the length of the first rectangle

Linear System:
We can create the two equations (a system) using the information from the problem:


Solve the system using Elimination or Substitution.

Isolate for x, in Equation #1:




Substitute this value into Equation #2:




Simplify the Equation:




Distribute the Parenthesis:




Add -24 to both sides:




Factor the Simple Trinomial:






Set Factors to equal 0:

First Factor:




Second Factor:




Since it is impossible to have a "negative length" the only possible answer would be:


Using this value, find the value of x:




Add -2 to both sides:




To find the area of the first rectangle, we can use a formula:


Input the values:


Simplify:


The Area of the First Rectangle is:


I hope this helped!
-Benjamin