Algebra II



Algebra II Name_________________________

Systems

NO CALCULATOR

Solve by graphing. Identify as consistent, inconsistent, independent, or dependent.

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Solve by Substitution.

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Solve by Elimination.

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Graph the following linear inequalities.

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Calculator

Solve the following problems by developing your own system of equations.

10. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 lb. mixture that is 12% protein?

Variables: x = _____________ System: ____________________

y= _____________ ____________________

Solution:

11. A train leaves a station traveling north at 75 km /h. Two hours later a second train leaves on a parallel track and travels north at 125 km/h. How far from the station will they meet?

Variables: x = _____________ System: _____________________

y = _____________ _____________________

Solution:

12. One day a store sold 45 pens, one kind at $8.50 and another kind at $9.75. In all $398.75 was taken in. How many of each kind were sold?

Variables: x = _____________ System: ___________________

y = _____________ ___________________

Solution:

13. Mr. Irwin and Mr. Lippi are math teachers. They have a total of 46 years of teaching. Two years ago Mr. Irwin had taught 2.5 times as many as Mr. Lippi. How long has each taught?

Variables: x = _____________ System: ________________________

y= _____________ ________________________

Solution:

14. The tens digit of a two digit positive integer is 2 more than three times the ones digit. If the digits are interchanged, the new number is 13 less than half the given number. Find the integer.

Variables: x = _____________ System: _____________________

y= ____________ _____________________

Solution:

15. Hank can row a boat 1 mile upstream in 24 minutes. He can row the same distance downstream in 13 minutes. If both the rowing speed and current speed are constant, find Hank’s rowing speed and the speed of the current.

Variables: x = _____________ System: ______________________

y = _____________ ______________________

Answer:

16. Pat picked strawberries on three days. He picked a total of 87 quarts. On Tuesday he picked 15 quarts

more than on Monday. On Wednesday he picked 3 quarts fewer than on Tuesday. How many quarts did

he pick each day?

Variables: x = __________ System: _________________________

y = __________ _________________________

z = __________ _________________________

Answer:

17. In a factory there are three polishing machines, A, B, and C. When all three of them are working, 5700 lenses can be polished in one week. When only A and B are working, 3400 lenses can be polished in one week. When only B and C are working, 4200 lenses can be polished in one week. How many lenses can be polished in one week by each machine?

Variables: x = __________ System: ______________________________

y = __________ ______________________________

z = __________ ______________________________

Answer:

Solve the following linear programming problems.

18. You are about to take a test that contains questions of type A worth 4 points and of type B worth 7 points. You must answer at least 5 of each type A and 3 of type B, but time restricts answering more than 10 of either type. In total, you can answer no more than 18. How many of each type of question must you answer, assuming all of your answers are correct, to maximize your score? What is the maximum score?

Variables: x = _____________ Constraints: _________________________________

y = _____________ _________________________________

_________________________________

Answer:

19. Mrs. Wood’s Biscuit factory makes two types of biscuits, Jumbos and Mini Mint. The oven can cook at most 200 biscuits per day. Jumbos require 2 ounces of flour while the Minis require only one ounce. There are 300 ounces of flour available. The income from the Jumbos is 10¢ each and the Mini Mints is 8¢. How many of each type should be baked to earn the greatest amount?

Assign Variables: x = ____________ Constraints: _________________________________

y = ____________ _________________________________

_________________________________

Answer:

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