### About Applications of Linear Equations Part 2:

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) One busy day, Pete's Sub Shaq sold a total of twenty-nine sandwiches. There were only two types of sandwiches sold. A turkey sandwich, which sold five more than the other: a tuna sandwich. How many of each type of sandwich was sold?

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#2:

Instructions: Solve each word problem.

a) Three sisters: Jamie, Stephanie, and Jill have a combined age of thirty-seven. If Jamie was one year younger, her sister Jill would be one-third her age. Jamie is seven years older than Stephanie. How old is each girl?

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#3:

Instructions: Solve each word problem.

a) At a computer store, a customer pleads to have a laptop sold for an all-inclusive price of four hundred twenty dollars. This price would include the twelve percent state and local taxes. If the manager allows this, what is the pre-tax price of the laptop?

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#4:

Instructions: Solve each word problem.

a) Jane won one hundred twenty thousand dollars in a lottery. She invested part at 3.5% annual simple interest and the rest at 9% annual simple interest. After two years, the total earnings were eighteen thousand three hundred dollars. How much was invested at each rate?

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#5:

Instructions: Solve each word problem.

a) John and Sam have two hundred twenty thousand dollars invested in bonds that pay 6% annual simple interest. How much additional money should be invested in a C.D. that pays 3% annual simple interest so that the total return on the two investments is 5.2%?

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Written Solutions:

#1:

Solutions:

a) Seventeen turkey sandwiches were sold, along with twelve tuna sandwiches.

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#2:

Solutions:

a) Jamie is nineteen years old, Stephanie is twelve years old, and Jill is six years old.

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#3:

Solutions:

a) The laptop’s pre-tax price would be three hundred seventy-five dollars.

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#4:

Solutions:

a) Thirty thousand dollars was invested at 3.5%, while ninety thousand dollars was invested at 9%.

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#5:

Solutions:

a) Eighty thousand dollars should be invested at 3% to make the total return 5.2%.