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 = [tex]=\pi r^{2}= \pi X5 X 5=78.5 square feet[/tex]
Area of Deck (in Gray) = (16 X 20) - ( [tex]\pi X5 X 5[/tex]) =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
