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Algebra / Linear equations in two variables Difficulty: Easy

A chemist studying the impact of salt on a process mixes $x$ kilograms of a low-salt mixture, which is $2 percent sign$ salt by weight, with $y$ kilograms of a high-salt mixture, which is $96 percent sign$ salt by weight, to create $24$ kilograms of a mixture that is $4 percent sign$ salt by weight. Which equation represents this situation?

$0.96 x + 0.02 y = (0.04) (24)$

$0.02 x + 0.96 y = (0.04) (24)$

$0.96 x + 0.02 y = 24$

$0.02 x + 0.96 y = 24$

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Explanation

Choice B is correct. It’s given that a chemist mixes $x$ kilograms of a low-salt mixture, which is $2 percent sign$ salt by weight. Multiplying $0.02$ by the amount of the low-salt mixture, $x$ kilograms, yields $0.02 x$ kilograms of salt in the low-salt mixture. It's also given that the chemist mixes $y$ kilograms of a high-salt mixture, which is $96 percent sign$ salt by weight. Multiplying $0.96$ by the amount of the high-salt mixture, $y$ kilograms, yields $0.96 y$ kilograms of salt in the high-salt mixture. Therefore, the total amount of salt in the combined mixture is $0.02 x plus 0.96 y$ kilograms. It's given that the low-salt mixture and the high-salt mixture together create $24$ kilograms of a combined mixture that is $4 percent sign$ salt by weight. Thus, the amount of salt in the combined mixture is $0.04 left parenthesis 24 right parenthesis$ kilograms. Since the total amount of salt in the combined mixture equals the amount of salt in the low-salt mixture and the amount of salt in the high-salt mixture, the equation $0.02 x + 0.96 y = (0.04) (24)$ represents this situation.

Choice A is incorrect. This equation represents a situation where the low-salt mixture is $96 percent sign$ , not $2 percent sign$ , salt by weight and the high-salt mixture is $2 percent sign$ , not $96 percent sign$ , salt by weight.

Choice C is incorrect. This equation represents a situation where the low-salt mixture is $96 percent sign$ , not $2 percent sign$ , salt by weight and the high-salt mixture is $2 percent sign$ , not $96 percent sign$ , salt by weight, and where the combined mixture contains $24$ kilograms of salt, not $24$ kilograms of a mixture that is $4 percent sign$ salt by weight.

Choice D is incorrect. This equation represents a situation where the combined mixture contains $24$ kilograms of salt, not $24$ kilograms of a mixture that is $4 percent sign$ salt by weight.