Question

In one day, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda. Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk. Marian consumes 510 calories by drinking 3 servings of milk and 1 soda. Using matrices to solve, how many calories are in 1 serving of milk?

Answer 1

Therefore, 110 calories are in 1 serving of milk.

Given, Joe consumes 530 calories by drinking 1 serving of juice, 2 servings of milk, and 1 soda.

Darius consumes 370 calories by drinking 2 servings of juice and 1 serving of milk.

Marian consumes 510 calories by drinking 3 servings of milk and 1 soda.

What are Linear Programming problems?

Linear programming, commonly known as LP, is a straightforward technique for representing complex real-world interactions by means of a linear function.

Now,

Let the calories in one serving of milk be x

Let the calories in one serving of juice be y

Let the calories in one serving of soda be z

For Joe, the equation to show the amount of calories is

2x + y + z = 530 -----(1)

For Darius, the equation to show the amount of calories is

x + 2y = 370 ------(2)

For Marian, the equation to show the amount of calories is

3x + z = 510 ------(3)

Now, y=370/2-x/2 and z=510-3x substitute in the equation 2x + y + z = 530.

2x+185-0.5x+510-3x=530

⇒695-1.5x=530

⇒1.5x=165

⇒x=110 calories

Hence, 110 calories are in 1 serving of milk.

To learn more about linear programming visit:

https://brainly.com/question/15417573.

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