Explanation Given Information: There are 800 calories, 55g of protein and 220mg of Vitamin C. The dietician prepares a meal of roast beef, baked potatoes, and asparagus according to the data provided in the table, Serving Size Calories Protein (in grams) Vitamin C (in milligrams) Roast beef, 3 oz. 300 20 0 Baked potato, 1 100 5 20 Asparagus, 180g 50 5 44 Formula used: To solve a system of linear equations with 3 unknowns, Step 1. Familiarize the variables. Step 2. Translate the given statements into numeric form. Step 3. Perform calculations to find the values of the 3 unknowns. Step 4. Check the solution. The distributive property of multiplication states that for terms a , b and c , a ⋅ ( b + c ) = a ⋅ b + a ⋅ c Calculation: Consider the table, Serving Size Calories Protein (in grams) Vitamin C (in milligrams) Roast beef, 3 oz. 300 20 0 Baked potato, 1 100 5 20 Asparagus, 180g 50 5 44 Consider the number of servings of roast beef to be x , the number of servings of baked beef to be y and the number of servings of asparagus to be z . There are 800 calories in total, which can be represented by the sum of the calories from each food, 300 x + 100 y + 50 z = 800 ………… ( 1 ) There are 55g of protein in total, which can be represented by the sum of the protein from each food, 20 x + 5 y + 5 z = 55 ………… ( 2 ) There are 220mg of Vitamin C in total, which can be represented by the sum of the Vitamin C from each food, 20 y + 44 z = 220 ………… ( 3 ) Multiply the above equation (2) by 15. 15 ( 20 x + 5 y + 5 z ) = 15 ( 55 ) Simplify using the distributive property, 15 ⋅ 20 x + 15 ⋅ 5 y + 15 ⋅ 5 z = 825 300 x + 75 y + 75 z = 825 ………… (4) Perform elimination of x by subtracting equation (1) from (4), 300 x + 75 y + 75 z = 825 − 300 x − 100 y − 50 z = − 800 − 25 y + 25 z = 25 Now, multiply the equation − 25 y + 25 z = 25 by 4, 4 ( − 25 y + 25 z ) = 4 ( 25 ) Simplify using the distributive property, 4 ⋅ ( − 25 y ) + 4 ⋅ 25 z = 100 − 100 y + 100 z = 100 ………… (5) Now, multiply the equation (3) by 5, 5 ( 20 y + 44 z ) = 5 ( 220 ) Simplify using the distributive property, 5 ⋅ ( 20 y ) + 5 ⋅ 44 z = 1100 100 y + 220 z = 1100 ………… (6) Now, perform elimination by addition of equations (5) and (6), 100 y + 220 z = 1100 − 100 y + 100 z = 100 320 z = 1200 Divide both sides by 320, 320 320 z = 1200 320 z = 15 4 Substitute 15 4 for z in (3), 20 y + 44 ( 15 4 ) = 220 20 y + 11 ⋅ 15 = 220 20 y + 165 = 220 Subtract 165 from both sides, 20 y + 165

6th Edition

ISBN: 9780321848741

Author: Marvin L. Bittinger

Publisher: PEARSON

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Chapter 8.5, Problem 24ES

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To calculate: The number of servings of each food, which is needed in order to satisfy the doctor’s orders.

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Chapter 8.5, Problem 23ES

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After taking a nutrition class, a big macaroni and cheese fan decides to improve the levels of protein and fiber in her favorite lunch by adding broccoli and canned chicken. The nutritional information for the foods referred to in this exercise is given in the table below. Complete parts (a) and (b) below. Nutrition Information per Serving Nutrient Calories Protein (g) Fiber (g) Mac and Cheese 268 11 2 Broccoli 50 5.3 5.1 Chicken 70 15 0 Shells 258 10 5 a. If she wants to limit her lunch to 400 calories but get 25 grams of protein and 10 grams of fiber, what proportions of servings of macaroni and cheese, broccoli, and chicken should she use? She should use servings of macaroni and cheese, servings of broccoli, and desired nutritional content. (Type an integer or decimal rounded to the nearest hundredth as needed.) servings of chicken to get her

After taking a nutrition class, a big macaroni and cheese fan decides to improve the levels of protein and fiber in her favorite lunch by adding broccoli and canned chicken. The nutritional information for the foods referred to in this exercise is given in the table below. Complete parts (a) and (b) below. Nutrition Information per Serving Nutrient Calories Protein (g) Fiber (g) Mac and Cheese 269 9 3 Broccoli 52 55 42 5.4 ܗ ܗ 5.2 Chicken 70 14 0 Shells 259 86 a If she wants to limit her lunch to 400 calories but get 35 grams of protein and 10 grams of fiber, what proportions of servings of macaroni and cheese, broccoli, and chicken should she use? She should use servings of macaroni and cheese, servings of broccoli, and servings of chicken to get her desired nutritional content. (Type an integer or decimal rounded to the nearest hundredth as needed)

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Chapter 8 Solutions

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Ch. 8.1 - In 2016, there were 35 species of amphibians in...Ch. 8.1 - 2. Refer to Example 2 . For another necklace, Star...Ch. 8.1 - Prob. 3YT Ch. 8.1 - Prob. 4YT Ch. 8.1 - Prob. 1ES Ch. 8.1 - Prob. 2ES Ch. 8.1 - Prob. 3ES Ch. 8.1 - Prob. 4ES Ch. 8.1 - Prob. 5ES Ch. 8.1 - Prob. 6ES

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The number of servings of each food, which is needed in order to satisfy the doctor’s orders.

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