Protein Supplements Exercises 45-48 are based on the following data on three popular protein supplements. (Figures shown correspond to a single serving)^{5}
Protein (g) | Carbohydrates (g) | Sodium (mg) | Cost ($) | |
Designer Whey (Next) | 18 | 2 | 80 | 0.50 |
Muscle Milk (Cytosport) | 32 | 16 | 240 | 1.60 |
Pure Whey Protein Stack (Champion) | 24 | 3 | 100 | 0.60 |
You have a mixture of Designer Whey and Pure Whey Protein Stack that costs a total of $14 and supplies exactly 540 grams of protein. How many grams of carbohydrates does it supply?
To calculate: The amount of carbohydrates in a mixture of Designer Whey and Pure Whey Protein Stack. The supplements, Designer Whey and Pure Whey Protein Stack are combined in such a way that the mixture costs
Protein (g) | Carbohydrates (g) | Sodium (mg) | Cost ($) | |
Designer Whey (Next) | ||||
Muscle Milk (Cytosport) | ||||
Pure Whey Protein Stack (Champion) |
Given Information:
In each serving, Designer Whey contains
Formula used:
Elimination method:
Step 1: Consider the linear equations in two variables.
Step 2: The equations are multiplied with suitable non-zero numbers to convert the coefficients to equals of opposite signs.
Step 3: The equations are combined to eliminate one variable, and the value of the other variable is calculated.
Step 4: Substitute the value of the calculated variable into one of the equations and calculate the value of the other variable.
Calculation:
Consider the problem,
In each serving, Designer Whey contains
Let x be the number of servings of Designer Whey and y be number of servings of Pure Whey Protein Stack.
Construct a table to represent the amount of the resources used,
Designer Whey (Next) | Pure Whey Protein Stack (Champion) | Total | |
Protein (g) | |||
Cost ($) |
Here, if x servings of Designer Whey is used and each serving contains
Also, if x servings of Designer Whey is used and each serving costs
Thus, the equation becomes,
Thus, the two equations are,
Consider the equation,
Divide both sides of the equation (1) by 6,
Consider the equation,
Multiply both sides of the equation (2) by
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