How many solutions exist for the given equation?
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Draw an illustration describing the problem as shown in the attached picture. The black box drawn represents the tank of water with dimensions labeled 30cm×48cm×36 cm. Jennifer and her friends threw heavy solid objects represented by the blue box. It has dimensions of 12cm×12m×20 cm. These boxes occupy the bottom of the tank up to a height of 28 cm drawn by the blue lines. Now, I think the question will be how many of those heavy solid objects will fill up the bottom of the tank. The other question would be, how much is the volume of water displaced by the heavy solid objects.
First, let's compute the volume of each solid object labeled as v.
v = 12×12×20
v = 2,880 cm³
Next, let's solve the volume to be filled up by these solid objects, labeled as V.
V = 30×48×28
V = 40,320 cm³
This is the volume of water displaced. When Jennifer and her friends drop the solid objects, each volume of object dropped corresponds to the same volume of water that overflows from the tank.
Next, we solve how many solid objects does it take to occupy 40,320 cm³.
Number of blocks = 40,320 cm³/2,880 cm³
Number of blocks = 14
Therefore, it would take 14 heavy solid objects to displace 40,320 cm³ of water.
First, let's compute the volume of each solid object labeled as v.
v = 12×12×20
v = 2,880 cm³
Next, let's solve the volume to be filled up by these solid objects, labeled as V.
V = 30×48×28
V = 40,320 cm³
This is the volume of water displaced. When Jennifer and her friends drop the solid objects, each volume of object dropped corresponds to the same volume of water that overflows from the tank.
Next, we solve how many solid objects does it take to occupy 40,320 cm³.
Number of blocks = 40,320 cm³/2,880 cm³
Number of blocks = 14
Therefore, it would take 14 heavy solid objects to displace 40,320 cm³ of water.