Question

(3.) If it costs $4.20 per square foot to installthe deck, what is the cost for plan A? PlanB?

Answer 1

Answer:

Step-by-step explanation:

I have reproduced a diagram of the question in the attachment.

To do a price comparison, we simply find the areas of both the deck and garden in Plan A and Plan B.

In Plan A,

Deck Measures 18 feet by 25 feet

Garden measures 9 feet by 12 feet

Area of Garden = 12 X 9 =108 square feet

Area of Deck (in Gray) = (18 X 25) - (12 X 9) =450-108 =342 square feet

Cost of Garden =$1.40 X 108=$151.2

Cost of Deck = $4.20 X 342=$1436.4

Total Cost for Plan A= $151.2+ $1436.4=$1587.6

In Plan B

Deck Measures 16 feet by 20 feet

Garden has a radius of 5 feet

Area of Garden = $=\pi r^{2}= \pi X5 X 5=78.5 square feet$

Area of Deck (in Gray) = (16 X 20) - ( $\pi X5 X 5$) =320-78.5 =241.5 square feet

Cost of Garden =$1.40 X 78.5=$109.9

Cost of Deck = $4.20 X 241.5=$1014.3

Total Cost for Plan B= $109.9+ $1014.3=$1124.2

Total Cost for Plan A=$1587.6

Total Cost for Plan B=$1124.2

Plan B is less expensive by $1587.6-$1124.2= $463.4