Question

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

The equation represents the relationship between these quantities.

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.

5 grams of protein and 2 grams of fat
10.5 grams of protein and 2 grams of fat
8 grams of protein and 4 grams of fat
If there are 6 grams of fat in the snack, how many grams of protein are there? Show your reasoning.
In this situation, what does a solution to the equation tell us? Give an example of a solution.

Answer 1

10.5 grams of protein and 2 grams of fat​ are the possible values of protein and fat based on the given algebraic equation.

If there are 6 grams of fat in the snack, using the algebraic equation, there would be 1.5 grams of protein in the cracker.

How to Analyze Relationships Using Algebraic Equations?

Given the algebraic equation that represents the relationship between the quantities of protein and fat contained in a snack as 4p + 9f = 60 , where f represents quantity of fat, and p represents the quantity of protein, to determine if each pair of values can be the number of protein and fat that are contained in the snack, substitute the given values into the algebraic equation.

If the right side of the equation and left side are equal, then the values for the number of grams for protein and fat are correct.

Given, p = 5, f = 2, substitute the values into 4p + 9f = 60:

4(5) + 9(2) = 60

38 ≠ 60 [not true]

Given, p = 10.5, f = 2, substitute the values into 4p + 9f = 60:

4(10.5) + 9(2) = 60

60 = 60 [true]

Given, p = 8, f = 4, substitute the values into 4p + 9f = 60:

4(8) + 9(4) = 60

68 ≠ 60 [not true]

Given, f = 6, substitute the value into 4p + 9f = 60 to find the grams of protein:

4p + 9(6) = 60

4p = 60 - 54

4p = 6

p = 1.5 grams of protein

This solution tells us that there are 1.5 grams of protein where you have 6 grams of fat in a cracker.

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