Question

The calorie count of a serving of food can be computed based on its composition of​ carbohydrate, fat, and protein. The calorie count C for a serving of food can be computed using the formula Chf​p, where h is the number of grams of carbohydrate contained in the​ serving, f is the number of grams of fat contained in the​ serving, and p is the number of grams of protein contained in the serving. Solve this formula for​ f, the number of grams of fat contained in a serving of food.

Answer 1

f =
`(1)/(9)` [C - 4(h - p)] grams

Explanation:

Given that:

C = 4h + 9f + 4p

where: C is the calorie count contained in the serving, h is the number of grams of carbohydrate contained in the​ serving, f is the number of grams of fat contained in the​ serving, and p is the number of grams of protein contained in the serving.

To solve for the number of grams of fat, then;

C - 4h - 4p = 9f

C - 4(h - p) = 9f

Divide through by 9, so that:

`(C - 4(h - p))/(9)` =
`(9f)/(9)`

`(C - 4(h - p))/(9)` = f

∴ f =
`(1)/(9)` [C - 4(h - p)]

The number of grams of fat, f, contained in a serving of food is
`(1)/(9)` [C - 4(h - p)]