y=4zx+7y = \dfrac{4z}{x+7}y=x+74zThe given equation relates the positive numbers x,y,x, y,x,y, and zzz. Which equation correctly expresses zzz in terms of xxx and yyy?Az=xy4z = \dfrac{xy}{4}z=4xyBz=x+74yz = \dfrac{x+7}{4y}z=4yx+7Cz=4yx+7z = \dfrac{4y}{x+7}z=x+74yDz=(x+7)y4z = \dfrac{(x+7)y}{4}z=4(x+7)yCheck answerShow answerExplanationWe start with y=4zx+7y = \dfrac{4z}{x+7}y=x+74z. Multiply both sides by (x+7)(x+7)(x+7): y(x+7)=4zy(x+7) = 4zy(x+7)=4z. Divide both sides by 4: z=(x+7)y4z = \dfrac{(x+7)y}{4}z=4(x+7)y. Thus, the correct answer is (x+7)y4\boxed{\dfrac{(x+7)y}{4}}4(x+7)y.
