\(\frac{2}{5}x= 16yw\) for some positive real numbers. If \(y\) is tripled and \(w\) is halved, by what percentage does x have to increase for the equation to be equal?
We have that 2x/5=16yw. If y is tripled and w is halved, then the new equation becomes [2x/5 = 16(3y)(w/2) = 24wy.]Dividing both sides by 5, we get [x/5 = 4wy.]Since the left side is 20% of the right side, x must be increased by 20%.
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