A deck is being built around a rectangular swimming pool. The swimming pool is 20 ft × 12 ft and the deck has a uniform width of 6 ft. What is the area of the deck only?
To find the area of the deck only, we need to calculate the area of the outer rectangle formed by the deck.
The length of the outer rectangle will be the length of the pool plus twice the width of the deck on either side:
Length of outer rectangle = 20 ft + 2 * 6 ft = 20 ft + 12 ft = 32 ft
Similarly, the width of the outer rectangle will be the width of the pool plus twice the width of the deck on either end:
Width of outer rectangle = 12 ft + 2 * 6 ft = 12 ft + 12 ft = 24 ft
Therefore, the area of the deck only is the area of the outer rectangle minus the area of the pool:
Area of deck only = Area of outer rectangle - Area of pool
= (32 ft * 24 ft) - (20 ft * 12 ft)
= 768 ft² - 240 ft²
= 528 ft²
So, the area of the deck only is 528 square feet.
A gym membership costs $25 to join and $14 each month. Write and use an algebraic expression to find the cost of the gym membership for 6 months.
To find the cost of the gym membership for 6 months, we need to multiply the monthly cost by 6 and add the initial joining cost.
Let's use the variables J and M to represent the joining cost and monthly cost, respectively.
J = $25 (joining cost)
M = $14 (monthly cost)
Then, the algebraic expression to find the cost of the gym membership for 6 months would be:
6M + J = 6 * $14 + $25
= $84 + $25
= $109
Therefore, the cost of the gym membership for 6 months would be $109.
To find the area of the deck only, we need to calculate the area of the outer rectangle formed by extending the dimensions of the pool by the deck width.
Step 1: Calculate the length and width of the outer rectangle:
Length of the outer rectangle = length of the pool + 2 * width of the deck
Width of the outer rectangle = width of the pool + 2 * width of the deck
Length of the outer rectangle = 20 ft + 2 * 6 ft = 20 ft + 12 ft = 32 ft
Width of the outer rectangle = 12 ft + 2 * 6 ft = 12 ft + 12 ft = 24 ft
Step 2: Calculate the area of the deck only:
Area of the deck only = Area of the outer rectangle - Area of the pool
Area of the deck only = Length of the outer rectangle * Width of the outer rectangle - Length of the pool * Width of the pool
Area of the deck only = 32 ft * 24 ft - 20 ft * 12 ft
Area of the deck only = 768 ft² - 240 ft² = 528 ft²
Therefore, the area of the deck only is 528 square feet.
To find the area of the deck only, we need to subtract the area of the pool from the overall area of the deck and pool combined.
To calculate the area of the deck and pool combined, we can find the length and width of the combined area by adding twice the width of the deck to the length and width of the pool.
The length of the combined area is 20ft + 2(6ft) = 20ft + 12ft = 32ft.
The width of the combined area is 12ft + 2(6ft) = 12ft + 12ft = 24ft.
The area of the deck and pool combined is 32ft × 24ft = 768ft².
To find the area of the pool only, we multiply the length and width of the pool: 20ft × 12ft = 240ft².
Finally, to find the area of the deck only, we subtract the area of the pool from the area of the deck and pool combined:
Deck Area = Deck and Pool Combined Area - Pool Area
= 768ft² - 240ft²
= 528ft².
Therefore, the area of the deck only is 528 square feet.