Question

the new shark tank at the city aquarium is in the shape of a rectangular prism. it is 87 ft long by 36 ft wide by 15 ft deep. to make the tank livable for the sharks, the aquarium workers treat the water using bags of salt. the amount of water a bag of salt can treat is known in cubic yards.
(a) find the volume of water in the tank in cubic yards. use the table of conversion facts, as needed.
( 3 \text{ yd} )
(b) to make the tank livable for the sharks, a bag of salt must be added for each ( 1.1 \text{ yd}^3 ) of water. the aquarium doesnt have any salt on hand and the salt can only be purchased in whole bags. how many bags of salt must be purchased to treat the water?
bags
(c) if each bag of salt costs $4.85, how much must the aquarium pay for salt to treat all the water in the new shark tank?
$

conversion facts for length
1 foot (ft) = 12 inches (in)
1 yard (yd) = 3 feet (ft)
1 yard (yd) = 36 inches (in)

Explanation:

Part (a)

Step1: Recall volume of rectangular prism

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height. Here, \( l = 87 \) ft, \( w = 36 \) ft, \( h = 15 \) ft. So, \( V = 87 \times 36 \times 15 \) cubic feet.
\( 87\times36 = 3132 \), \( 3132\times15 = 46980 \) cubic feet.

Step2: Convert cubic feet to cubic yards

Since \( 1 \) yard \( = 3 \) feet, \( 1 \) cubic yard \( = 3^3 = 27 \) cubic feet. So, to convert cubic feet to cubic yards, divide by \( 27 \).
\( \text{Volume in cubic yards} = \frac{46980}{27} \)
\( 46980\div27 = 1740 \) cubic yards.

Step1: Determine number of bags needed

Each bag treats \( 1.1 \) cubic yards. Let \( n \) be the number of bags. Then \( n=\frac{\text{Total volume}}{\text{Volume per bag}}=\frac{1740}{1.1} \)
\( 1740\div1.1\approx1581.82 \)

Step2: Round up (since we need whole bags)

Since we can only purchase whole bags, we round up to the next whole number. So \( n = 1582 \) bags.

Step1: Calculate total cost

Each bag costs \( \$4.85 \), and we need \( 1582 \) bags. Total cost \( = 1582\times4.85 \)
\( 1582\times4.85 = 1582\times(4 + 0.8 + 0.05)=1582\times4 + 1582\times0.8 + 1582\times0.05 = 6328 + 1265.6 + 79.1 = 7672.7 \)

Answer:

\( 1740 \) cubic yards

Part (b)