### About Applications of Linear Equations Part 3:

When solving a word problem, the most important step is to understand the main objective. This gives the student a laser focus. We can then filter through all of the information, leading to an equation that can be solved. We then provide an answer and check to make sure it is reasonable.

Test Objectives

- Demonstrate the ability to read a word problem and understand the main objective
- Understand how to set up an equation based on the information given in a word problem
- Demonstrate the ability to check the solution to a word problem

#1:

Instructions: Solve each word problem.

a) How many pounds of mixed nuts that contain 42% peanuts must Jimmy add to eight pounds of mixed nuts that contain 20% peanuts to make a mixture that is 34% peanuts?

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#2:

Instructions: Solve each word problem.

a) A metallurgist needs to make 16.5 pounds of an alloy containing 78% nickel. She is going to melt and combine one alloy that is 76% nickel with another alloy that is 82% nickel. How much of each should she use?

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#3:

Instructions: Solve each word problem.

a) A cashier received a total of six hundred seventy-nine dollars in $1, $5, and $20 bills only. There were a total of sixty-three bills received. The number of $1 bills received was two-thirds of the number of $5 bills received. How many of each type of bill was received?

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#4:

Instructions: Solve each word problem.

a) Beth made a trip to the lake and back. The trip there took two hours and the trip back took three hours. She averaged 30 mph on the return trip. Find the average speed of the trip there.

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#5:

Instructions: Solve each word problem.

a) Jane left the hospital and traveled toward her cabin on the lake at an average speed of 74 mph. Kristin left 0.9 hours later and traveled in the opposite direction with an average speed of 55.8 mph. Find the number of hours Kristin needs to travel before they are 326.2 miles apart.

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Written Solutions:

#1:

Solutions:

a) Jimmy needs to use fourteen pounds of the mixed nuts that are 42% peanuts.

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#2:

Solutions:

a) She needs eleven pounds of the metal that is 76% nickel, along with 5.5 pounds of the metal that is 82% nickel.

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#3:

Solutions:

a) There were a total of twenty-one $5 bills, fourteen $1 bills, and twenty-eight $20 bills.

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#4:

Solutions:

a) The average speed of the trip there was 45 mph.

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#5:

Solutions:

a) Kristen needs to travel for two hours before they are 326.2 miles apart.