SOLUTION: If A varies directly to x and A varies inversely to y.If x varies directly to t and y varies directly to t.Find how A varies to t

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Question 815469: If A varies directly to x and A varies inversely to y.If x varies directly to t and y varies directly to t.Find how A varies to t
Answer by jsmallt9(3758) (Show Source):
You can put this solution on YOUR website!
From "A varies directly to x" we get:

(I'm using subscripts on the constants of variation because there are more than one and I want to name them as k's.)
From "x varies directly to t" we get:

We are looking for how A varies to t. So we do not want x in the equation. The second equation is already solved for x. Using this we can substitute into the first equation for x:

or

Since and are constants, so it their product. So if we let our equation becomes:

which is an equation of direct variation. So A varies directly with t.