A fish tank weighs 80 pounds when 40% full of water, and it weighs 140 pounds when completely full. How many pounds does the tank weigh when empty?
Okay, so you have two variables, let's call them x and y. x will be the weight of the water when the tank is full, and y will be the weight of the tank.
So you can get two equations from the question:
.4x+y=80 (1)
x+y=140 (2)
and now you can do elimination by subtracting (1) from (2).
x+y-(.4x+y)=140-80
so you get
.6x=60
then divide by .6 to get
x=100
and since you want y, sub x=100 into (2)
100+y=140
y=140-100
y=40
So the tank weighs 40 pounds when empty.
Sorry if this is a little long (I wasn't sure how much detail is too much, you see)
To find out how much the tank weighs when empty, we can start by finding out how much water it can hold.
Let's assume that the weight of the water in the tank increases linearly with the fill level. In other words, if the tank weighs 80 pounds when it's 40% full, we can find out how much it would weigh when it's 100% full.
First, we need to find the weight of the tank with 100% water. The difference in weight between the tank when it's 100% full and when it's 40% full is 140 - 80 = 60 pounds.
Since this difference represents 60% of the total water weight, we can set up the following equation:
60 pounds = 60% of the total water weight
To find the total water weight, we divide both sides of the equation by 0.60:
60 pounds / 0.60 = total water weight
Now, we can calculate the total water weight:
total water weight = 100 pounds
Next, we need to figure out the weight of the empty tank. We can do this by subtracting the weight of the water from the weight of the full tank:
weight of empty tank = weight when full - weight of water
weight of empty tank = 140 pounds - 100 pounds
weight of empty tank = 40 pounds
Therefore, the tank weighs 40 pounds when it's empty.