12 gallons of water fill a tank to 3\4 capacity. A . What is the capacity of the tank?
B .If the tank is then filled to capacity, how many half-gallon bottles can be filled with the water in the tank.

Answer:

A. 16, B.32

Step-by-step explanation:

A.

We will say that is the total capacity of the tank.

Since 12 gallons of water fill the tank to 3/4 capacity, we know that 12 gallons is 3/4 of the total capacity. Hence,

.

The last equation tells us that .

B.

We will say that D is the number of half-gallon bottles that can be filled with the water of the tanke, note that D times 1/2 must be the total capacity of the tank. Hence,

and so, we get that

A. The capacity of the tank is 16 gallons.

B. If the tank is filled to capacity, it can fill 32 half-gallon bottles

Given information:

The tank is filled with 12 gallons of water, which is 3/4 of its capacity.

To find the capacity of the tank and the number of half-gallon bottles that can be filled when the tank is full.

Step 1: A.

Calculate the total capacity of the tank:

• Since the tank is currently filled to 3/4 of its capacity,  set up the equation:

           3/4 capacity = 12

• To find the capacity, multiply both sides by 4/3:

• capacity =

       On multiplying gives:

• capacity =

      On dividing by 3 gives:

• capacity = 16 gallons

Step 2: B.

Calculate the number of half-gallon bottles that can be filled when the tank is full:

• Since the tank has a capacity of 16 gallons, and each bottle is half a gallon, divide the capacity by 1/2:

• bottles =

      On taking the reciprocal of the denominator, gives:

• bottles =
• On
• multiplying
• gives:

• bottles = 32 bottles

Therefore, the capacity of the tank is 16 gallons, and when the tank is filled to capacity, it can fill 32 half-gallon bottles with water.

Learn more about capacity and conversions here:

brainly.com/question/33454758

#SPJ6