### About Applications of Linear Systems:

In many cases, word problems will involve more than one unknown. When we solve a problem with more than one unknown, it will sometimes be necessary to set up a system of equations that relate the two or more unknown quantities. For these types of problems, we begin by reading the problem carefully. We must understand the objective of the problem. We then assign variables to represent the unknowns. The next step is to set up a system of linear equations. These are based on the information given to us in the problem. We then solve the system and state the answer. With any word problem, we state our answer in a nice, clear, and concise sentence or paragraph (if needed). Lastly, we want to check the result. We want to ensure that our answer is reasonable in terms of the problem. We also want to make sure that the math works out, by checking our result based on the structure of the problem.

Test Objectives

- Demonstrate the ability to solve a word problem that involves a linear system

#1:

Instructions: solve each word problem.

a) The senior classes at Madison High School and James Woods High School planned separate trips to the water park. The senior class at Madison High School rented and filled 7 vans and 7 buses with 280 students. James Woods High School rented and filled 3 vans and 4 buses with 154 students. Each van and each bus carried the same number of students. Find the number of students in each van and in each bus.

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#2:

Instructions: solve each word problem.

a) Tim and Shawn each improved their yards by planting daylilies and shrubs. They bought their supplies from the same store. Tim spent $111 on 9 daylilies and 6 shrubs. Shawn spent $153 on 7 daylilies and 13 shrubs. What is the cost of one daylily and the cost of one shrub?

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#3:

Instructions: solve each word problem.

a) A plane traveled 1320 miles each way to Phoenix and back. The trip there was with the wind. It took 11 hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of the plane in still air? What is the speed of the wind?

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#4:

Instructions: solve each word problem.

a) Nicole and Danielle are selling cookie dough for a school fundraiser. Customers can buy packages of white chocolate chip cookie dough and packages of gingerbread cookie dough. Nicole sold 7 packages of white chocolate chip cookie dough and 6 packages of gingerbread cookie dough for a total of $76. Danielle sold 9 packages of white chocolate chip cookie dough and 11 packages of gingerbread cookie dough for a total of $124. What is the cost each of one package of white chocolate chip cookie dough and one package of gingerbread cookie dough?

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#5:

Instructions: solve each word problem.

a) Jennifer is trying to eat a meal with 66 grams of protein, 94.5 grams of carbohydrates, and 910 milligrams of calcium. At the local diner, they are serving only turkey, potatoes, and yogurt. Each serving of turkey contains 30 grams of protein, 35 grams of carbohydrates, and 200 milligrams of calcium. Each serving of potatoes has 3 grams of protein, 16 grams of carbohydrates, and 10 milligrams of calcium. Lastly, each serving of yogurt has 9 grams of protein, 13 grams of carbohydrates, and 300 milligrams of calcium. How many servings of each food should Jennifer consume?

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Written Solutions:

#1:

Solutions:

a) Van: 6 students, Bus: 34 students

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#2:

Solutions:

a) daylily: $7, shrub: $8

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#3:

Solutions:

a) plane: 93 mph, wind: 27 mph

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#4:

Solutions:

a) white chocolate chip cookie dough: $4, gingerbread cookie dough: $8

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#5:

Solutions:

a) 1.5 servings of turkey, 1 serving of potatoes, and 2 servings of yogurt