Question

A rectangular garden has a walkway around it. The area of the garden is 6(6.5x + 2.5). The combined area of the garden and the walkway is 6.5(8x + 6). Find the area of the walkway around the garden as the sum of two terms.

Answer 1

According to the information given in the exercise, the following expression represents the area of the rectangular garden:

$6\mleft(6.5x+2.5\mright)$

And the following expression represents the combined area of the walkway around the rectangular garden and the area of the garden:

$6.5\mleft(8x+6\mright)$

You can identify that the word "combined" indicates that that expression was obtained by adding both areas.

Knowing the above, you can set up the following equation:

$6(6.5x+2.5)+A=6.5(8x+6)$

Where "A" is the area of the walkway around the rectangular garden.

Solving for "A", you get the following expression:

$\begin{gathered} A=6.5(8x+6)-6(6.5x+2.5) \\ A=52x+39-39x-15 \\ A=13x+24 \end{gathered}$

The answer is:

$13x+24$