Unit: Linear Systems

Lesson: Solving a Linear System of Equations using Linear Combination

ASSIGNMENT (9 points)

Answer Key

(3 points)

1.  Mr. Smith bought 8 tacos and 2 burritos for his family. His total cost was $11. Mr. Jones bought 5 tacos and 6 burritos for his family and spent $14. Find the cost of a taco and the cost of a burrito.

·  Write a system of equations to represent the situation described in the problem.

Let t = the price of one taco.

Let b = the price of one burrito. (Choice of variables may vary.)

·  Use the linear combination method to find the solution for the system. Use mathematics to explain how you obtained the solution. Use words, symbols, or both in your explanation.

Explanations may vary depending upon factors used to multiply the equations.

The solution is (1, 1.5) or $1 for tacos and $1.50 for burritos.

·  What is the cost of a taco and what is the cost of a burrito?

The price of a taco is $1 and the price of a burrito is $1.50.

(4 points)

2.  Harrison has 8 coins in his pocket. Some are quarters and some are dimes. He has no other types of coins. The value of the coins in his pocket is $1.55. How many of each does he have?

·  Write a system of equations to represent the situation described in the problem.

Let q = the number of quarters and d = the number of dimes. (Choice of variables may vary.)

·  Use linear combination to solve the system. Use mathematics to explain how you arrived at the solution. Use words, symbols, or both in your explanation.

Explanations may vary depending upon factors used to multiply equations in order to solve the system.

The solution is (5, 3) or 5 quarters and 3 dimes.

·  How many of each type of coin does Harry have? Use mathematics to justify your answer.

Harry has 5 quarters and 3 dimes.

The total number of coins is 5 + 3 = 8 coins.

The total value of his coins is $1.55 since

(2 points)

3.  Ms. Winfrey ordered 2 computers and 10 graphing calculators for her students. The total cost of her order was $1950. Mr. Reed ordered 3 computers and 6 graphing calculators for his students at a cost of $2160. What was the cost of one graphing calculator? Use mathematics to explain your answer. Use words, symbols, or both in your explanation.

Let c = the price of one computer and g = the price of one graphing calculator. (Choices for variables may vary.)

Explanations may vary depending upon the choice of factors by which to multiply the equations.

The price of one graphing calculator is $85.