Question 1100495: Hi
a tank with a square base of sides 10cm was 3/4 filled with water. Half the amount of water was poured into an empty container filling it to the brim.two thirds of the amount of water in the container
was poured into a basin which was already one fifth filled with 700cm^3 of water. The basin was then half full.
what was the original water level in the tank
what was the height of the tank.
Thanks
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! let T be the amount of water that the tank can hold.
let C be the amount of water that the container can hold.
let B be the amount of water that the basin can hold.
the tank is 3/4 filled with water, therefore you start with 3/4 * T.
you pour half the amount of water that's in the tank into a container and the container is filled to the brim.
therefore C = 1/2 * 3/4 * T which becomes:
C = 3/8 * T
you pour 2/3 of the water that's in the container into the basin which already has 700 cm^3 of water in it and the basin becomes half full.
therefore 2/3 * C + 700 = 1/2 * B
you are told that 700 cm^3 of water equals 1/5 the amount of water that the basin can hold.
therefore, the amount of water that the basin can hold is 5 * 700 = 3500 cm^3 of water.
therefore B = 3500
from the equation of 2/3 * C + 700 = 1/2 * B, replace B with 3500 to get:
2/3 * C + 700 = 1/2 * (3500) which becomes:
2/3 * C + 700 = 1750
solve for C to get:
C = (1750 - 700) / (2/3) = 1575
from the equation of C = 3/8 * T, replace C with 1575 to get:
1575 = 3/8 * T
solve for T to get:
T = 1575 / (3/8) which becomes:
T = 4200
the original amount of water that was in the tank was 3/4 * 4200 = 3150 cm^3.
the volume of water in the tank is given by the formula:
V = area of the base * the height.
the area of the base is 10 * 10 = 100 cm^2.
the formula becomes 4200 = 100 * the height.
the height of the tank is therefore equal to 4200 / 100 = 42 cm.
the height of the original water level in the tank would be 3/4 * 42 = 31.5 cm.
to confirm if the solution is correct, do the following.
the tank is 3/4 full, therefore the amount of water in the tank is 3/4 * 4200 = 3150 cm^3.
you fill the container with half of this, therefore the amount of water in the container is 1/2 * 3150 = 1575 cm^3.
you take 2/3 of this and add it to 700 cm^3 of water already in the basin and you get 2/3 * 1575 + 300 = 1750 cm^3 of water in the basin.
this amount of water makes the basin half full, therefore a full basin of water can hold 2 * 1750 = 3500 cm^3 of water.
1/5 of this is 3500 / 5 = 700 cm^3 of water which is what you were given.
everything checks out so the solution looks good.
the height of the original amount of water in the tank was 31.5 cm.
the height of the full tank was 42 cm.
the original amount of water in the tank was 3150 cm^3.
the full capacity of the tank was 4200 cm^3.
that's what i get.
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