Section 3.6 More Applications of Linear Systems

3.6 Lecture Guide: More Applications of Linear Systems Objective: Use systems of linear equations to solve word problems.

Strategy for Solving Word Problems Step 1. Read the problem carefully to determine what you are being asked to find. Step 2. Select a variable to represent each unknown quantity. Specify precisely what each variable represents and note any restrictions on each variable. Step 3. If necessary, make a sketch and translate the problem into word equations. Then translate the word equations into a system of algebraic equations. Step 4. Solve the equation or the system of equations, and answer the question asked by the problem. Step 5. Check the reasonableness of your answer.

1. Marlon is making a picture frame out of wood molding. He has 42 inches of molding to create the frame. If the width of the frame must be 5 inches less than the length, what will be the dimensions of the frame? Will a 9 inch by 12 inch picture fit in this frame? (a) Select a variable to represent each of the unknown quantities and identify each variable, including the units of measurement. (b)Write a system of algebraic equations.

1. Marlon is making a picture frame out of wood molding. He has 42 inches of molding to create the frame. If the width of the frame must be 5 inches less than the length, what will be the dimensions of the frame? Will a 9 inch by 12 inch picture fit in this frame? (c)Solve this system of equations.

1. Marlon is making a picture frame out of wood molding. He has 42 inches of molding to create the frame. If the width of the frame must be 5 inches less than the length, what will be the dimensions of the frame? Will a 9 inch by 12 inch picture fit in this frame? (d) Is this solution within the restrictions on the variables and does it seem reasonable?

1. Marlon is making a picture frame out of wood molding. He has 42 inches of molding to create the frame. If the width of the frame must be 5 inches less than the length, what will be the dimensions of the frame? Will a 9 inch by 12 inch picture fit in this frame? (e)Write a sentence that answers the problem.

2. The bill for a cellular phone in August was $10 more than twice the September bill. The total that was required to pay both of these bills was $175. What was the bill for each month? (a) Select a variable to represent each of the unknown quantities and identify each variable.

2. The bill for a cellular phone in August was $10 more than twice the September bill. The total that was required to pay both of these bills was $175. What was the bill for each month? (b) Write a system of algebraic equations and solve the system.

2. The bill for a cellular phone in August was $10 more than twice the September bill. The total that was required to pay both of these bills was $175. What was the bill for each month? (c) Write a sentence that answers the problem and make sure the answer is reasonable and within the restrictions on the variables.

Rate Principle Applications of the Rate Principle

3. A small t-shirt screening business operates on a daily fixed cost plus a variable cost that depends on the number of shirt screened in one day. The total cost for screening 260 shirts on Friday was $1015. The total cost for screening 380 shirts on Saturday was $1345. What is the fixed daily cost? What is the cost to screen each shirt? (a) Select a variable to represent each of the unknown quantities and identify each variable.

3. A small t-shirt screening business operates on a daily fixed cost plus a variable cost that depends on the number of shirt screened in one day. The total cost for screening 260 shirts on Friday was $1015. The total cost for screening 380 shirts on Saturday was $1345. What is the fixed daily cost? What is the cost to screen each shirt? (b) Write a system of algebraic equations and solve the system.

3. A small t-shirt screening business operates on a daily fixed cost plus a variable cost that depends on the number of shirt screened in one day. The total cost for screening 260 shirts on Friday was $1015. The total cost for screening 380 shirts on Saturday was $1345. What is the fixed daily cost? What is the cost to screen each shirt? (c) Write a sentence that answers the problem and make sure the answer is reasonable and within the restrictions on the variables.

Mixture Principle for Two Ingredients Amount in first + Amount in second = Amount in mixture Applications of the Mixture Principle 1. Amount of product A + Amount of product B = Total amount of mixture 2. Variable cost + Fixed cost = Total cost 3. Interest on bonds + Interest on CDs = Total interest 4. Distance by first plane + Distance by second plane = Total distance 5. Antifreeze in first solution + Antifreeze in second solution = Total amount of antifreeze

4. The Candy Shop has two popular kinds of candy. The owner is trying to make a mixture of 100 pounds of these candies to sell at $3 per pound. If the gummy gums are priced at $2.50 per pound and the sweet treats are $3.75 per pound, how many pounds of each must be mixed in order to produce the desired amount?

5. Ashley invested money in two different accounts. One investment was at 10% simple interest and the other was at 12% simple interest. The amount invested at 10% was $ more than the amount invested at 12%. The total interest earned was $ How much money did Ashley invest in each account?

6. A hospital needs 80 liters of a 12% solution of disinfectant. This solution is to be prepared from a 33% solution and a 5% solution. How many liters of each should be mixed to obtain this 12% solution?

7. Sue and Jennifer decided to get together one weekend for a visit. They live 472 miles apart. They both left their homes at 8:00 a.m. on Saturday and drove toward each other. Sue drove 6 mph faster than Jennifer and they met in 4 hours. How fast were they each driving?