Question

a rectangular garden has a walkway around it. the area of the garden is 6(4.5x + 2.5). the combined area of the garden and the walkway is 1.5(20x + 6). find the area of the walkway around the garden as the sum of two terms.

the area of the walkway around the garden is
(simplify your answer. use integers or decimals for any numbers in the expression.)

Explanation:

Step1: Define walkway area formula

Area of walkway = Combined area - Garden area

Step2: Substitute given expressions

$\text{Walkway Area} = 7.5(8x + 6) - 6(4.5x + 2.5)$

Step3: Expand both products

$= (7.5 \times 8x + 7.5 \times 6) - (6 \times 4.5x + 6 \times 2.5)$
$= (60x + 45) - (27x + 15)$

Step4: Distribute the negative sign

$= 60x + 45 - 27x - 15$

Step5: Combine like terms

$= (60x - 27x) + (45 - 15)$
$= 33x + 30$

Answer:

$33x + 30$