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Perry wants to increase their protein intake for a diet. They find a good protein bar that contains 15g of protein per serving. They also find a good protein shake that contains 24g of protein per serving. If Perry wants to add 165g of protein to their diet each week, how many servings of each do they need per week to meet all their protein goals in 8 servings?

Respuesta :

We need 3 servings of protein bars and 5 servings of protein shakes per week.

Given,

Protein bar = 15g of protein per serving.

Protein shake = 24g of protein per serving.

165g of protein is required each week.

Total number of servings = 8

We need to find how many servings of each are needed per week to meet 165g of protein.

How do solve a system of equations?

By substitution method.

Let us consider two systems of equations:

x + y = a ____(1)

x + 2y = b ____(2)

From (1) we have,

x = a - y

Putting this in (2) we get,

a - y + 2y = b

y = b - a

Let us consider,

Protein bar servings be x.

Protein shake servings be y.

Make two systems of equations.

x + y = 8 _____(A)

15x + 24y = 165 ______(B)

Solve by substitution method.

From (A),

x = 8 -y

Putting in (B)

15(8-y) + 24y = 165

120 - 15y + 24y = 165

120 + 9y = 165

Subtracting 120 on both sides.

9y = 165 - 120

9y = 45

Dividing both sides by 9

y = 45/9 = 5

We have,

y = 5 putting in (A)

x + y = 8

x = 8 - 5

x = 3.

We can cross-check:

- x + y = 8

5 + 3 = 8

8 = 8

- 15x + 24y = 165

15 x 3 + 24 x 5 = 165

45 + 120 = 165
165 = 165

Thus we need 3 servings of protein bars and 5 servings of protein shakes per week.

Learn more about solving a system of equations here:

https://brainly.com/question/27911202

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