11-15-2015, 09:41 PM

Topic 2: Try Out Your Skills

Pick one of the problems in the attached file (at end of this message). Solve it using a system of linear equations, showing details of how you set up your equations and the steps that you went through for the solution. You must use one of the methods in your Unit 2 Lesson (Addition/Subtraction, Substitution, Graphical Method) in order to get credit for this forum so you may want to complete your reading assignment before you attempt your post. See the attached file with a sample of a worked problem.

If you need assistance, please ask for assistance from me or from one of your fellow students. The problem must be solved using one of our accepted methods - substitution, elimination or graphically. When you have solved the problem, post your complete solution.

Instructions: Please make the title for your post the problem number so that other people can tell at a glance which problems have been done. Only the first person to post a solution will get credit for the problem, so be sure that you are not duplicating another classmate's work.

Your initial post should be at least 250 words. Please respond to at least 2 other students. Your responses may be to assist your fellow student with their problem (although you should refrain from solving the entire problem for them) or to show an alternative method that could be used to solve the problem. An acceptable response may also be to ask for further clarification on any part of their solution. Other acceptable responses would be to pose situations where you could use this methodology for real-world problems so that a discussion may develop about the value/applicability of this methodology to the situation. Responses should be a minimum of 100 words and may include direct questions.

Initial Post Due: Thursday, by 11:55pm, ET

Responses Due: Sunday, by 11:55pm, ET

Forum #2: Linear Equations in Real Life

Pick one of the following problems. Show how you would solve it using a system of linear equations.

1) John spent $201 shirts and pants for work. Shirts cost $27 and pants cost $22. If he bought a total of 8

articles of clothing, then how many of each kind did he buy?

2) A school dance has 228 students. There are 63 fewer girls than twice as many boys. How many boys and

girls attended the dance?

3) There are 15 animals in the barn. Some are ducks and some are pigs. There are 46 legs in all. How many of

each animal are there?

4) The sum of two numbers is 66. The larger number is three more than twice the smaller number. Find the

numbers.

5) A police academy is training 14 new recruits. Some are working dogs and others are police officers. There

are 38 legs in all. How many of each type of recruit are there?

6) A Boy Scout troop carries 57 boys on a trip in 8 vehicles. Each van can carry 14 boys, while each car can

carry 3 boys. How many vans and how many cars did the troop take?

7) A high school purchases two workbooks for every textbook, and two journals for every workbook. If the

school purchases 301 total items, how many of each do they need?

8) A mom bought 28 packages of Reese’s Cups with 88 total cups. Each king size package holds 4 cups.

Each regular size package holds two cups. How many of each size did she buy?

9) A high school marching band of 205 students went to a competition. They took 9 vehicles, some cars and

some buses. Find the number of cars and the number of buses they took if each car holds 5 students and

each bus hold 45 students.

10) The sum of three numbers is 47. One number is three more than the smallest number, and one number is

twice the smallest number. What are the numbers?

11) A textbook publisher has two kinds of printing presses: Model A which can print 60 books per day and

Model B which can print 65 books per day. The company owns 13 total printing presses and this allows

them to print 800 books per day. How many of each type of press do they have?

12) A school copier can print 5 copies of a test per minute and 8 copies of a quiz per minute. If I make 167

copies in 25 minutes, how many of each did I copy?

13) A supermarket had a one day sale on Coke products. It sold three times as many two-liter bottles of Coke as

Coke Zero, and twice as many two-liter bottles of Diet Coke as Coke Zero. If the supermarket sold 612

two-liter bottles in one day, how many of each did it sell?

14) At a football game, a dad purchases hot dogs for $1.25 and drinks for $1.75. If he purchases 9 items for

$13.25, how many of each did he purchase?

15) A church group attends a play. Tickets cost $6.50 for youth and $7.50 for adults. If 20 people went for

$137, how many youth and adults attended?

16) Two brothers live two miles from school. The older brother leaves school riding his bicycle at 8 miles an

hour. The younger brother leaves home at the same time to meet him riding at 4 miles per hour. A bee

travels back and forth between them at 9 miles/hour. How far will the bee fly before the brothers meet?

17) Gas costs $3.89 for unleaded and $4.09 for premium. If I buy 37 gallons of gas for $148.93, how much of

each type of gas do I buy?

18) Mechanical pencils cost 13 cents each and wooden pencils cost 4 cents each. If I purchase 200 pencils for

$12.23, how many of each do I purchase?

19) Two different kinds of grass seed are to be mixed to produce 4 pounds of four that is valued at $3.00

/pound. If the value of the premium seed is $3.50 and the price of the regular seed is $2.70, how many

pounds of each type should go into the mixture?

20) A large group goes to a restaurant and orders chicken dinners for $8 and steak dinners for $9. If 27 people

spend $235, how many have chicken and steak?

21) An adult has 32 teeth. A child has 28 teeth. If 43 people have 1,288 teeth, how many are adults and how

many are children?

22) According to the U.S. Mint, a half dollar weighs 11.34 grams and a dollar coin weighs 8.1 grams. If 28

coins weigh 285.12 grams, what is the value of the change?

23) According to the U.S. Mint, a penny weighs 2.5 grams and a nickel weighs 5 grams. If 27 pennies and

nickels weigh 117.5 grams, what is the value of the change?

24) A high speed train travels from Chicago to Denver at an average speed of 90 miles per hour, but can make

the return trip at an average speed of 110 miles per hour. What is the average speed for the round trip?

25) A man can harvest his farm in 18 hours. His son can harvest the same farm in 12 hours. How long will it

take them working together?

26) There are 43 cars in the parking lot. Some are two-door coupes and some are four-door sedans. If there are

116 doors, how many of each type of car are in the parking lot?

27) The United States Air Force Academy has two sizes of classrooms. The typical classrooms have 24 seats.

The engineering classrooms 32 seats. If one wing has 16 classrooms with 424 seats, how many of each

classroom does the wing have?

28) The sum of two numbers is 41. The smaller number is five more than half the larger number. Find the

numbers.

29) A train leaves the station at 7:00 A.M. traveling west at 80 mi/h. On a parallel track, a second train leaves

the station 3 hours later traveling west a 100 mi/h. At what time will the second train catch up with the

first?

30) Dave works at the mall part-time for $9 per hour and notices that 20% of his check is deducted for taxes. If

he wants to take home at least $200 per week, how many hours does he have to work?

Pick one of the problems in the attached file (at end of this message). Solve it using a system of linear equations, showing details of how you set up your equations and the steps that you went through for the solution. You must use one of the methods in your Unit 2 Lesson (Addition/Subtraction, Substitution, Graphical Method) in order to get credit for this forum so you may want to complete your reading assignment before you attempt your post. See the attached file with a sample of a worked problem.

If you need assistance, please ask for assistance from me or from one of your fellow students. The problem must be solved using one of our accepted methods - substitution, elimination or graphically. When you have solved the problem, post your complete solution.

Instructions: Please make the title for your post the problem number so that other people can tell at a glance which problems have been done. Only the first person to post a solution will get credit for the problem, so be sure that you are not duplicating another classmate's work.

Your initial post should be at least 250 words. Please respond to at least 2 other students. Your responses may be to assist your fellow student with their problem (although you should refrain from solving the entire problem for them) or to show an alternative method that could be used to solve the problem. An acceptable response may also be to ask for further clarification on any part of their solution. Other acceptable responses would be to pose situations where you could use this methodology for real-world problems so that a discussion may develop about the value/applicability of this methodology to the situation. Responses should be a minimum of 100 words and may include direct questions.

Initial Post Due: Thursday, by 11:55pm, ET

Responses Due: Sunday, by 11:55pm, ET

Forum #2: Linear Equations in Real Life

Pick one of the following problems. Show how you would solve it using a system of linear equations.

1) John spent $201 shirts and pants for work. Shirts cost $27 and pants cost $22. If he bought a total of 8

articles of clothing, then how many of each kind did he buy?

2) A school dance has 228 students. There are 63 fewer girls than twice as many boys. How many boys and

girls attended the dance?

3) There are 15 animals in the barn. Some are ducks and some are pigs. There are 46 legs in all. How many of

each animal are there?

4) The sum of two numbers is 66. The larger number is three more than twice the smaller number. Find the

numbers.

5) A police academy is training 14 new recruits. Some are working dogs and others are police officers. There

are 38 legs in all. How many of each type of recruit are there?

6) A Boy Scout troop carries 57 boys on a trip in 8 vehicles. Each van can carry 14 boys, while each car can

carry 3 boys. How many vans and how many cars did the troop take?

7) A high school purchases two workbooks for every textbook, and two journals for every workbook. If the

school purchases 301 total items, how many of each do they need?

8) A mom bought 28 packages of Reese’s Cups with 88 total cups. Each king size package holds 4 cups.

Each regular size package holds two cups. How many of each size did she buy?

9) A high school marching band of 205 students went to a competition. They took 9 vehicles, some cars and

some buses. Find the number of cars and the number of buses they took if each car holds 5 students and

each bus hold 45 students.

10) The sum of three numbers is 47. One number is three more than the smallest number, and one number is

twice the smallest number. What are the numbers?

11) A textbook publisher has two kinds of printing presses: Model A which can print 60 books per day and

Model B which can print 65 books per day. The company owns 13 total printing presses and this allows

them to print 800 books per day. How many of each type of press do they have?

12) A school copier can print 5 copies of a test per minute and 8 copies of a quiz per minute. If I make 167

copies in 25 minutes, how many of each did I copy?

13) A supermarket had a one day sale on Coke products. It sold three times as many two-liter bottles of Coke as

Coke Zero, and twice as many two-liter bottles of Diet Coke as Coke Zero. If the supermarket sold 612

two-liter bottles in one day, how many of each did it sell?

14) At a football game, a dad purchases hot dogs for $1.25 and drinks for $1.75. If he purchases 9 items for

$13.25, how many of each did he purchase?

15) A church group attends a play. Tickets cost $6.50 for youth and $7.50 for adults. If 20 people went for

$137, how many youth and adults attended?

16) Two brothers live two miles from school. The older brother leaves school riding his bicycle at 8 miles an

hour. The younger brother leaves home at the same time to meet him riding at 4 miles per hour. A bee

travels back and forth between them at 9 miles/hour. How far will the bee fly before the brothers meet?

17) Gas costs $3.89 for unleaded and $4.09 for premium. If I buy 37 gallons of gas for $148.93, how much of

each type of gas do I buy?

18) Mechanical pencils cost 13 cents each and wooden pencils cost 4 cents each. If I purchase 200 pencils for

$12.23, how many of each do I purchase?

19) Two different kinds of grass seed are to be mixed to produce 4 pounds of four that is valued at $3.00

/pound. If the value of the premium seed is $3.50 and the price of the regular seed is $2.70, how many

pounds of each type should go into the mixture?

20) A large group goes to a restaurant and orders chicken dinners for $8 and steak dinners for $9. If 27 people

spend $235, how many have chicken and steak?

21) An adult has 32 teeth. A child has 28 teeth. If 43 people have 1,288 teeth, how many are adults and how

many are children?

22) According to the U.S. Mint, a half dollar weighs 11.34 grams and a dollar coin weighs 8.1 grams. If 28

coins weigh 285.12 grams, what is the value of the change?

23) According to the U.S. Mint, a penny weighs 2.5 grams and a nickel weighs 5 grams. If 27 pennies and

nickels weigh 117.5 grams, what is the value of the change?

24) A high speed train travels from Chicago to Denver at an average speed of 90 miles per hour, but can make

the return trip at an average speed of 110 miles per hour. What is the average speed for the round trip?

25) A man can harvest his farm in 18 hours. His son can harvest the same farm in 12 hours. How long will it

take them working together?

26) There are 43 cars in the parking lot. Some are two-door coupes and some are four-door sedans. If there are

116 doors, how many of each type of car are in the parking lot?

27) The United States Air Force Academy has two sizes of classrooms. The typical classrooms have 24 seats.

The engineering classrooms 32 seats. If one wing has 16 classrooms with 424 seats, how many of each

classroom does the wing have?

28) The sum of two numbers is 41. The smaller number is five more than half the larger number. Find the

numbers.

29) A train leaves the station at 7:00 A.M. traveling west at 80 mi/h. On a parallel track, a second train leaves

the station 3 hours later traveling west a 100 mi/h. At what time will the second train catch up with the

first?

30) Dave works at the mall part-time for $9 per hour and notices that 20% of his check is deducted for taxes. If

he wants to take home at least $200 per week, how many hours does he have to work?