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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

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 determine

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 $14 and supplies exactly 540 grams of protein. The following table shows the data on the three protein supplements correspond to a single serving.

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
Explanation

Given Information:

In each serving, Designer Whey contains 18 grams of protein and 2 grams of carbohydrates. In each serving, Pure Whey Protein Stack contains 24 grams of protein and 3 grams of carbohydrates. In each serving, Designer Whey costs $0.50 and Pure Whey Protein Stack costs $0.60. The mixture costs a total of $14 and supplies exactly 540 grams of protein.

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 18 grams of protein and 2 grams of carbohydrates. In each serving, Pure Whey Protein Stack contains 24 grams of protein and 3 grams of carbohydrates. In each serving, Designer Whey costs $0.50 and Pure Whey Protein Stack costs $0.60. The mixture costs a total of $14 and supplies exactly 540 grams of protein.

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) 18 24 540
Cost ($) 0.50 0.60 14

Here, if x servings of Designer Whey is used and each serving contains 18 g of protein, and if y servings of Pure Whey Protein Stack is used and each serving contains 24 g of protein, then a total of protein used is 18x+24y grams. But the mixture supplies exactly 540 grams of protein. Thus, the equation becomes,

18x+24y=540

Also, if x servings of Designer Whey is used and each serving costs $0.50 and if y servings of Pure Whey Protein Stack is used, and each serving costs $0.60, then the total mixture costs 0.50x+0.60y dollars. But the mixture costs a total of $14.

Thus, the equation becomes,

0.50x+0.60y=14

Thus, the two equations are,

18x+24y=540 …… (1)

0.50x+0.60y=14 …… (2)

Consider the equation,

18x+24y=540

Divide both sides of the equation (1) by 6,

186x+246y=54063x+4y=90

Consider the equation,

0.50x+0.60y=14

Multiply both sides of the equation (2) by 10 to get rid of decimals,

10(0.50x+0.60y)=10(14)10(0.51)x+10(0

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