5x + 4y +3z = 14 x = 3z -22 z = 6 What is the y-value of the solution?
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The tank with Chemical X "takes up" a space of 25ft³. Ordinarily we think of something "taking up" space as being area or surface area; however, area is a square measurement, and this is cubic; this must be volume. The volume of the tank with Chemical X is 1.5 times the volume of the tank containing Chemical Y; setting this up in an equation we would have
25 = 1.5<em>V</em>
We would divide both sides by 1.5 to get the volume of the tank containing Chemical Y:
To find the volume of a cylinder, we find the base area and multiply by the height. We know the volume and we know the base area, so our equation to find the height of the tank containing Chemical Y would look like:
We would now divide both sides by 3 2/10:
This is the same as:
So the height of the tank containing Chemical Y is 500/96 = 5 5/24 feet.
25 = 1.5<em>V</em>
We would divide both sides by 1.5 to get the volume of the tank containing Chemical Y:
To find the volume of a cylinder, we find the base area and multiply by the height. We know the volume and we know the base area, so our equation to find the height of the tank containing Chemical Y would look like:
We would now divide both sides by 3 2/10:
This is the same as:
So the height of the tank containing Chemical Y is 500/96 = 5 5/24 feet.