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:
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