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3.1 Ratios, Rates, and Proportional Relationships - Direct/inverse proportionality
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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 x food calories is equivalent to k kilojoules, of the following, which best represents the relationship between x and k ?

 

A.

k equals zero point 2 4 x

B.

k equals 4 point 2 x

C.

x equals 4 point 2 k

D.

x k equals 4 point 2

The table above gives the typical amounts of energy per gram, expressed in both food calories

Hard-difficulty · SAT Math · Ratios, Rates, and Proportional Relationships — Direct/inverse proportionality. Read the question above, select your answer, and check the full explanation below to understand exactly why the correct choice works.

Answer explanation

Choice B is correct. The relationship between x food calories and k kilojoules can be modeled as a proportional relationship. Let the ordered pair x sub 1 comma k sub 1 and the ordered pair x sub 2 comma k sub 2 represent the values in the first two rows in the table: the ordered pair 4 point 0 comma 16 point 7 and the ordered pair 9 point 0 comma 37 point 7. The rate of change, or the fraction with numerator, k sub 2 minus k sub 1, and denominator x sub 2 minus x sub 1, end fraction, is 21 over 5 equals 4 point 2; therefore, the equation that best represents the relationship between x and k is k equals 4 point 2 x.

Choice A is incorrect and may be the result of calculating the rate of change using the fraction with numerator, x sub 2 minus x sub 1, and denominator k sub 2 minus k sub 1, end fraction. Choice C is incorrect because the number of kilojoules is greater than the number of food calories. Choice D is incorrect and may be the result of an error when setting up the equation.

 

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