# Algebra Question

Here I will need for you to turn this problem in to a algebra problem with work shown according to the attachment  I HAVE ATTACH A SAMPLE OF WHAT THIS SHOULD LOOK LIKE

I have attach the directions and the applications sheet

Problem:

Jamil always throws loose change into a pencil holder on his desk and

takes it out every two weeks. This time it is all nickels and dimes. There

are 2 times as many dimes as nickels, and the value of the dimes is \$1.65

more than the value of the nickels. How many nickels and dimes does

Jamil have?

Forum: If Only I Had a System…

Applications of Systems of Linear Equalities

The Problem:

When students are surveyed about what makes a good math Forum, at least half of the responses involve

 “discussing how to work problems”  “seeing how this math applies to real-life situations”

This Forum on applications of systems of equations addresses both of these concerns.

Unfortunately, the typical postings are far from ideal.

This is an attempt to rectify the situation. Please read this in its entirety before you

Pick-up games in the park vs. the NBA:

Shooting hoops in the park may be lots of fun, but it scarcely qualifies as the precision play of a well-coached team. On the one hand, you have individuals with different

approaches and different skill levels, “doing their own thing” within the general rules of the game. On the other hand you have trained individuals, using proven strategies and basing their moves on fundamentals that have been practiced until they are second

nature.

The purpose of learning algebra is to change a natural, undisciplined approach to

individual problem solving into an organized, well-rehearsed system that will work on many different problems. Just like early morning practice, this might not always be pleasant; just like Michael Jordan, if you put in the time learning how to do it correctly, you will score big-time in the end.

But my brain just doesn’t work that way. . .

Nonsense! This has nothing to do with how your brain works. This is a matter of learning to read carefully, to extract data from the given situation and to apply a

mathematical system to the data in order to obtain a desired answer. Anyone can learn to do this. It is just a matter of following the system; much like making cookies is a matter of following a recipe.

“Pick-up Game” Math

It is appalling how many responses involve plugging in numbers until it works.

 “My birthday is the eleventh, so I always start with 11 and work from there.”

 “The story involved both cats and dogs so I took one of the numbers, divided by 2 and then I experimented.”

 “First I fire up Excel…”

 “I know in real-life that hot dogs cost more than Coke, so I crossed my fingers and started with \$0.50 for the Coke…”

The reason these “problem-solving” boards are moderated is so that these creative souls don’t get everyone else confused!

NBA Math

In more involved problems, where the answer might come out to be something irrational, like the square root of three, you are not likely to just randomly guess the

correct answer to plug it in. To find that kind of answer by an iterative process (plugging and adjusting; plugging and adjusting; …) would take lots of tedious work or a computer. Algebra gives you a relative painless way of achieving your objective without wearing

The reason that all of the homework has involved x’s and y’s and two equations, is that

we are going to solve these problems that way. Each of these problems is a story about two things, so every one of these is going to have an x and a y.

In some problems, it’s helpful to use different letters, to help keep straight what the variables stand for. For example, let L = the length of the rectangle and W = the width.

The biggest advantage to this method is that when you have found that w = 3 you are more likely to notice that you still haven’t answered the question, “W hat is the length of

the rectangle?” Here are the steps to the solution process:

 Figure out from the story what those two things are.

o one of these will be x

o the other will be y

 The first sentence of your solution will be “Let x = ” (or “Let L = ” )

o Unless it is your express purpose to drive your instructor right over the edge, make sure that your very first word is “Let”

 The second sentence of your solution will be “Let y = ” (or “Let W = ” )

 Each story gives two different relationships between the two things.

o Use one of those relationships to write your first equation.

o Use the second relationship to write the second equation.

 Now demonstrate how to solve the system of two equations. You will be using

either

o substitution

o or elimination – just like in the homework.

More examples…

For this problem, I’d use substitution to solve the system of equations:

The length of a rectangle blah, blah, blah…

Let L = the length of the rectangle

… blah, blah, blah twice the width

Let W = the width of the rectangle

The length is 6 inches less than twice the width

L = 2W – 6

The perimeter of the rectangle is 56

2L + 2W =56

For this one, I’d use elimination to solve the system of equations:

Blah, blah, blah bought 2 cokes…

Let x = the price of a coke

.. blah, blah, blah 4 hot dogs

Let y = the price of a hot dog

2 cokes plus 4 hot dogs cost 8.00

2x + 4y = 8.00

3 cokes plus 2 hot dogs cost 8.00

3x + 2y = 8.00

For this one, I’d use substitution to solve the system of equations:

One number is blah, blah, blah…

Let x = the first number

…blah, blah, blah triple the second number

Let y = the second number

The first number is triple the second

x = 3y

The sum of the numbers is 24

x + y = 24

The problem: Two numbers add to give 4 and subtract to give 2. Find the numbers.

Solving the problem:

Let x = the first number

Let y = the second number

Two numbers add to give 4: x + y = 4

Two numbers subtract to give 2: x – y = 2

Our two equations are: x + y = 4 x – y = 2 Adding the equations we get

2x = 6

x = 3 The first number is 3.

x + y = 4 Substituting that answer into equation 1

3 + y = 4

y = 1 The second number is 1.

Two numbers add to give 4: 3 + 1 = 4

The two numbers subtract to give 2: 3 – 1 = 2

Do NOT demonstrate how to check the answers that are provided and call that

demonstrating how to solve the problem!

Formulas vs. Solving equations

Formulas express standard relationships between measurements of things in the real world and are probably the mathematical tools that are used most frequently in real -life situations.

Solving equations involves getting an answer to a specific problem, sometimes based on real-world data, and sometimes not. In the process of solving a problem, you may

need to apply a formula. As a member of modern society, it is assumed that you know certain common formulas such as the area of a square or the perimeter of a rectangle. If you are unsure about a formula, just Google it. Chances are excellent it will be in one of

the first few hits.

If you are still baffled:

 W atch a lecture on “Applications of Systems of Equations”

 W atch this video: Solve applications of systems of linear equations or inequalities

 View the PowerPoint Presentations that are provided in the link from the Lesson section.

 Message me if you are still confused.

 Topic: Week 5: If Only I Had a System… ( 3 messages – 3 unread ) New messages 1. 1. 1. This will be your opportunity to be the teacher. Click on “View Full Description and attachments” below for the directions and questions. Be sure to open the file called “MATH110 Read This First.pdf” before you jump in! View Full Description and attachments Hide Full Description and attachments Read the attached files. First read the one entitled “Read this first” and then open the file called “Systems of Equations Problems with Answers” Pick ONE of the problems that has not already been solved, and demonstrate its solution for the rest of us. Select Start a New Conversation and make the problem number and topic (#10 Jarod and the Bunnies) the subject of your post. The answers are at the end of the file, so don’t just give an answer—we can already see what the answers are. Don’t post an explanation unless your answer matches the correct one! This is a moderated forum. Your posting will not be visible to the rest of the class until I approve it. Occasionally, more than one person will tackle a problem before they can see the work of others. In that case, credit will be given to all posters. Once the solution to a problem has become visible, that problem is off limits and you will need to choose a different problem in order to get credit. I will indicate in the grading comments if corrections need to be made. If you haven’t received credit, first double-check for my comments in the gradebook. If everything looks OK, then message me asking me to check on it. You must make the necessary corrections and have your work posted in order to receive credit.  Your initial post is worth 10 points. It is not necessary to respond to 2 classmates on this forum although a request for clarification on the procedure used would be appropriate. Also, I’m sure that a “thank you” for an exceptionally clear explanation would be welcome!

SAMPLE QUESTION WITH PROBLEM THIS IS WHAT I NEED.

A tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 4 soft drinks for \$36.12. The second group bought 6 slices of pizza and 6 soft drinks for \$31.74. How much does one slice of pizza cost?

The equation will be solved by using elimination.

Let x = the cost of a slice of pizza Let y = the cost of a soft drink

8x+4y=36.12 6x+6y=31.74

The least common multiple of 4 and 6 is 12. Multiply the first equation by 3 and the second equation by 2, by doing so that will have the y variable eliminated when the second equation is subtracted from the first equation.

(3)8x + (3)4y = (3)36.12 which solves to 24x + 12y = 108.36 (2)6x + (2)6y = (2)31.74 which solves to 12x + 12y = 63.48

Subtract the second equation from the first and solve for x.

24x + 12y = 108.36 -12x – 12y = 63.48 12x = 44.88 divide by sides by 12 to solve for x 12 12 x = 3.74

A single slice of pizza costs \$3.74. If you want to continue through the equation and find the cost for a single soft drink, you can substitute x into the first equation and solve for the y variable.

8(3.74) + 4y = 36.12 29.92 + 4y = 36.12 then subtract 29.92 from both sides of the equation -29.92 = -29.92 4y = 6.20 then divide by sides by 4 to solve for y 4 4 y = 1.55

A single soft drink costs \$1.55.

The cost of a single slice of pizza is \$3.74 and the cost of a single soft drink is \$1.55.

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