Question

One gram of protein contains 4 calories. One gram of fat contains 9 calories. A snack has 60 calories from p grams of protein and f grams of fat.

The equation 4p+9f=60 represents the relationship between these quantities.

1. Determine if each pair of values could be the number of grams of protein and fat in the snack. Be prepared to explain your reasoning.

A. 5 grams of protein and 2 grams of fat

B. 10.5 grams of protein and 2 grams of fat

C. 8 grams and 4 grams of fat

2. If there are 6 grams of fat in the snack, how many grams of protein are there? Show your reasoning.

3. In this situation, what does a solution to the equation 4p + 9f = 60 tell us? Give an example of a solution.

Answer 1

Answer:

Step-by-step explanation:

Equation representing the relationship between the calories from Protein and fat is,

6p + 9f = 60

1). A). If p = 5 grams  and f = 2 grams,

        Number of calories = (6×5) + (9×2)

                                         = 30 + 18

                                         = 48 calories

  B). If p = 10.5 grams  and f = 2 grams,

        Number of calories = (6×10.5) + (9×2)

                                         = 63 + 18

                                         = 81 calories

  C). If p = 8 grams and f = 4 grams

        Number of calories = (6×8) + (9×4)

                                         = 48 + 36

                                         = 84 calories

(2). If f = 6 grams, then we have to calculate the grams of protein from the given equation.

    4p + (9×6) = 60

    4p + 54 = 60

    4p = 60 - 54

    p = $\frac{6}{4}=1.5$ grams

(3). Combination of 6 grams of fat and 1.5 grams of protein in a snack gives 60 calories of energy.