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Algebra / Linear equations in two variables Difficulty: Easy

A mixture consisting of only vitamin D and calcium has a total mass of $150$ grams. The mass of vitamin D in the mixture is $50$ grams. What is the mass, in grams, of calcium in the mixture?

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Explanation

Choice C is correct. Let $d$ represent the mass, in grams, of vitamin D in the mixture, and let $c$ represent the mass, in grams, of calcium in the mixture. It’s given that the mixture consists of only vitamin D and calcium and that the total mass of the mixture is $150$ grams. Therefore, the equation $d + c = 150$ represents this situation. It’s also given that the mass of vitamin D in the mixture is $50$ grams. Substituting $50$ for $d$ in the equation $d + c = 150$ yields $50 + c = 150$ . Subtracting $50$ from both sides of this equation yields $c equals 100$ . Therefore, the mass of calcium in the mixture is $100$ grams.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect. This is the total mass, in grams, of the mixture, not the mass, in grams, of calcium in the mixture.

Choice D is incorrect. This is the mass, in grams, of vitamin D in the mixture, not the mass, in grams, of calcium in the mixture.