Question

Mr and Mrs.Haprer Are planning to install a deck and a garden Help them determine which of the two choices below is most cost officiant The deck is shown in Gray The Garden is shown in White

Answer 1

Part 1 (Area of the Garden)

In Plan A. the garden measures 9 ft by 12 ft.

`\begin{gathered} \text{Area of the garden in Plan A=}_{}9*12 \\ =108ft^2 \end{gathered}`

In Plan B, the garden has a radius of 5 ft.

`\begin{gathered} \text{Area of the garden in Plan B=}_{}\pi r^2 \\ =\pi*5^2 \\ =25\pi ft^2 \end{gathered}`

Part 2 (Area of the Deck)

Area of the Deck = Area of the outer shape-Area of the garden

Plan A

`\begin{gathered} \text{Area of the deck=}(18*25)-108 \\ =450-108 \\ =342ft^2 \end{gathered}`

Plan B

`\begin{gathered} \text{Area of the deck=(16x20)-25}\pi \\ =241.46ft^2 \end{gathered}`

Part 3

It costs $4.20 per square foot to install the deck:

`\begin{gathered} \text{Cost of Plan A=342 x 4.20 =\$1436.40} \\ \text{Cost of Plan B=241.46 x 4.20 =\$1}014.13 \end{gathered}`

Part 4

It costs $1.40 per square foot to install the garden:

`\begin{gathered} \text{Cost of Plan A=108 x 1.40 =\$}151.20 \\ CostofPlanB=25\pi*\text{ 1.40 =\$1}09.96 \end{gathered}`

Part 5

We calculate the total costs

`\begin{gathered} Total\; c\text{ost of Plan A=1}436.40+151.20=1587.60 \\ Cost\; of\; PlanB=1014.13+\text{1}09.96=1124.09 \end{gathered}`

We see that Plan B is less expensive by:

`\begin{gathered} 1587.60-1124.09 \\ =\$463.51 \end{gathered}`