Ask a question

Story Problem

A dietician is preparing a meal for a client with the following dietary needs from the meal: 581 calories, 20.24 g of fat, and 53.08 g of protein. The meal will consist of chicken, baked potatoes, and broccoli.

Each serving of chicken contains 250 calories, 13 g of fat, and 30 g of protein.
Each baked potato contains 161 calories, 0.2 g of fat, and 4.3 g of protein.
Each serving of broccoli contains 50 calories, 0.6 g of fat, and 4.2 g of protein.

Determine the number of servings of each food that the dietician will need to prepare for this dinner. How many servings of broccoli will be in this dinner?

1 Answer by Expert Tutors

Tutors, sign in to answer this question.
Suneil P. | Knowledgeable and Passionate University of Pennsylvania Math TutorKnowledgeable and Passionate University ...
5.0 5.0 (25 lesson ratings) (25)
This is a linear system of equations!!!
Call unknowns or things you are trying to solve for variables...that is a start.
For instance, call the number of servings of chicken x, that of potato y, and that of broccoli z.
We seek a specific coordinate or combination (x,y,z) so that we obtain exactly the calories, grams of fat, and grams of protein specified.
We can write an equation for each specification.
For instance, to specify the need of 581 cal, given our variables, we can write : 250x+161y+50z=581.
Likewise you can write equations for the others, solve the linear system of 3 eq'ns (matrices may help...or not), and then solve for broccoli :)