A water tank is 18 full. The tank is 34 full when 42 gallons of water are added to the tank.
a. How much water can the tank hold?
The tank can hold ____ gallons of water.
b. How much water was originally in the tank?
The tank originally held ____ gallons of water.
c. How much water is in the tank when it is 1/2 full?
The tank holds ______ gallons of water when it is 1/2 full.
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18 = 1/8 maybe?
if so then (6/8) t = (1/8) t + 42
5/8 t = 42
t = 67.2 gallons full
(1/8 ) t = 8.4 gal when 1/8 full
t/2 = 33.6 gal half full
To solve this problem, we'll use a ratio and proportion approach. Let's go step by step to find the answers to each question:
a. To find out how much water the tank can hold, we'll set up a proportion using the given data. Let's call the maximum capacity of the tank "x" gallons. We know that when the tank is 18 full, it contains 18 gallons of water. When the tank is 34 full, it contains 42 gallons of water. So, we can set up the following proportion:
18 / x = 34 / 42
To solve for x, we can cross-multiply and then solve for x:
18 * 42 = 34 * x
756 = 34x
Divide both sides by 34:
756 / 34 = x
x ≈ 22.24
Therefore, the tank can hold approximately 22.24 gallons of water.
b. Now, let's find out how much water was originally in the tank. We know that when the tank is 18 full, it contains 18 gallons of water. Using the calculated maximum capacity from part (a), which is approximately 22.24 gallons, we can subtract the water added later:
22.24 - 18 = 4.24
Therefore, the tank originally held approximately 4.24 gallons of water.
c. To find out how much water is in the tank when it is 1/2 full, we need to determine half of the maximum capacity calculated in part (a).
1/2 * 22.24 ≈ 11.12
Therefore, the tank holds approximately 11.12 gallons of water when it is 1/2 full.