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Algebra / Linear functions Difficulty: Hard

The figure presents a 3-column table, with 3 rows of data, titled “Energy per Gram of Typical Macronutrients.” The heading for column 1 is “Macronutrient,” the heading for column 2 is “Food calories,” and the heading for column 3 is “Kilojoules.” The 3 rows of data are as follows. Row 1.Macronutrient, Protein; Food calories, 4 point zero; Kilojoules, 16 point 7. Row 2. Macronutrient, Fat; Food calories, 9 point zero; Kilojoules, 37 point 7. Row 3. Macronutrient, Carbohydrate; Food calories, 4 point zero; Kilojoules, 16 point 7.

The table above gives the typical amounts of energy per gram, expressed in both food calories and kilojoules, of the three macronutrients in food. If the 180 food calories in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydrate, which of the following expresses f in terms of p and c ?

 

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Explanation

Choice B is correct. It is given that there are 4.0 food calories per gram of protein, 9.0 food calories per gram of fat, and 4.0 food calories per gram of carbohydrate. If 180 food calories in a granola bar came from p grams of protein, f grams of fat, and c grams of carbohydrate, then the situation can be represented by the equation 180 equals, 4 p plus 9 f, plus 4 c. The equation can then be rewritten in terms of f by subtracting 4p and 4c from both sides of the equation and then dividing both sides of the equation by 9. The result is the equation f equals, 20 minus, four ninths times, open parenthesis, p plus c, close parenthesis.

Choices A, C, and D are incorrect and may be the result of not representing the situation with the correct equation or incorrectly rewriting the equation in terms of f.