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Algebra / Linear equations in two variables Difficulty: Medium

A batch of banana milkshakes consists of $4$ cups of ice cream and $2$ bananas and has $1,114 milligrams left parenthesis mg right parenthesis$ of calcium. There is $276 mg$ of calcium in $1$ cup of the ice cream used to make this batch of milkshakes. How much calcium, $in mg$ , is in $1$ banana?

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Explanation

Choice A is correct. It’s given that a batch of banana milkshakes consists of $4$ cups of ice cream and $2$ bananas and has $1,114$ mg of calcium. It’s also given that there is $276$ mg of calcium in $1$ cup of the ice cream used to make this batch of milkshakes. It follows that the total amount of calcium in $4$ cups of ice cream is $4 left parenthesis 276 right parenthesis$ , or $1,104$ mg. Let $x$ represent the amount of calcium, in mg, in $1$ banana. It follows that the total amount of calcium in $2$ bananas is $2 x$ mg. Since the batch of banana milkshakes has $1,114$ mg of calcium, the equation $1,104 + 2 x = 1,114$ represents this situation. Subtracting $1,104$ from both sides of this equation yields $2 x equals 10$ . Dividing both sides of this equation by $2$ yields $x equals 5$ . Therefore, the amount of calcium in $1$ banana is $5$ mg.

Choice B is incorrect. This is the amount of calcium, in mg, in $2$ bananas, not in $1$ banana.

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

Choice D is incorrect. This is the amount of calcium, in mg, in $4$ cups of ice cream, not in $1$ banana.