7.6 More Rate Problems Practice & Start of Mixtures (7.7)

As you come in today, please start with your classwork:

CW: 7.6 Word Problem Practice - Rates 3

Please attempt the rate problems on this worksheet.  Hopefully you are getting more familiar with setting up rate problems.  If not, please watch this video of me solving #1.

 Once you have finished the classwork, you can start on your homework:

HW: 7.6 Word Problem Practice - Rates 4b and pg 421 #s 25 & 26

Please attempt #1 and #2 on your own.  Both have to do with rates of speed affected by waves or wind.  These are similar to your homework from last night.  However #2 has an interesting twist which will require you to go back to the work we did with:

DISTANCE = RATE x TIME

Please watch these videos of me solving #1 and #2 if you need help.

Once you have completed these you can attempt #3, a mixture problem.  For support you can choose to watch a video of me solving #3 or look in your textbook on pg 418.

7.6 More Rate Problems

Today we will review last night's homework problems.  As you can see the level of difficulty is ratcheting up but you are ready for it (even if you don't believe that yet).  I've listed how things are getting more challenging and the tools you have to meet the challenge:

• the problems require more translating from English into algebraic terms
1. use grids to break down the word problems
2. list information
3. rewrite tasks or questions
4. use the info and question to determine what answer you are seeking
5. label the answer with variables
6. go back and use the information to do the work and create linear equations that will help you solve for the variables

• the calculations are starting to involve more decimals or fractions. This is all the pre-algebra rational number work that can get tricky:
• with fractions you can multiply through BOTH sides of the equations to change fractions to whole numbers
• maintain your number sense while you do your fraction or decimal work 
• i.e. 1.9 X 1.2 approximates to 2 X 1 
• so when you get the answer of 228 you should know that you can place the decimal between the 2s
• the answer would be 2.28
• use a calculator to check your answers

After we are finished reviewing, you can start the next concept related to rates which focuses more on currents.  Please watch me solving the first part of the Rate w. Currents problem on the back of your classwork page.  Be sure you take notes and turn it in for full credit.

Then you can begin your homework:

HW: pg 415-17 #s 17, 21, 24

7.6 Word Problems w Systems of Linear Equations involving Rates

We've done some practice of translating word problems from the English language into Algebra language over the past few weeks.  Recently I challenged you to translate the guacamole and salsa word problem from pg 403 in our textbook.  Working on translating will help you as we move into word problems with rates.

Please watch the video of me solving #2 of your classwork page.  Watch it a second time and take notes on your classwork page.  Then write equations for #1 and solve using elimination, substitution or graphing.  

IF YOU NEED HELP WITH ANY OF THE CLASSWORK AND THE VIDEO IS NOT WORKING FOR YOU PLEASE LET ME KNOW.

After that please watch me solving #3(a) of your classwork.  Watch it a second time and take notes.  Then solve 3b on your own.  

Once you have completed the classwork page (including copying notes), please bring it to me and you can start your homework for tonight:

HW pg 416 #s 18, 19, 22 (show grids, equations & solve for all including 18)

7.2 to 7.4 Quiz Tomorrow

Just reminding you that we have a quiz tomorrow.  You will need to show that you can solve problems algebraically in the following ways:

1. graphing the equations for the common solution
2. using substitution to solve the system of equations
3. using elimination (starting by multiplying) to solve the system of equations

Please be sure to do the Practice Quiz - Homework.  I am attaching videos below of the solutions for those problems.  My suggestion would be to watch the video after you attempt the homework, similarly to how we reviewed the Practice Quiz - Classwork in class today.

HW: 7.2, 7.3, 7.4 Quiz - Practice Quiz Homework

Videos of Solutions to Practice Quiz - Homework

1. solving systems of equations by graphing
2. solving systems of equations by substitution
3. solving systems of equations by elimination

If you still have questions, please feel free to email me:

jadams@a-cs.org

See you tomorrow!

7.4 Solve Word Problems with Systems of Linear Equations by Multiplying & Eliminating

Since most people do not get paid simply for solving systems of linear equations, we will now practice the algebraic work we have done multiplying and eliminating with word problems.

Accordingly we will use grids to help us disaggregate the data we find in the word problems, translate the words into algebraic equations and then solve using appropriate steps to eliminate variables.

Start by practicing elimination with multiplication:

HW: pg 402 #s 20, 21, 22

Then, follow my lead by taking notes while you watch me solve #33 of your HW.

HW: pg 402-3 #s 33*, 34, 35, 39** (grid, equations & solve by elimination) 

**For number 39, be sure to graph your answer as well.

7.4 Solving Systems of Equations by Multiplying and Eliminating

Just like it says in the title, we are moving into solving systems of equations by multiplying and eliminating.  Sounds difficult, but you already know most of the steps to do this.

Quick review:

They need two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. They went on 4 rides altogether.  

First,

Two tickets for ride on the bumper cars and 3 tickets for each ride on the ferris wheel for a total of ten tickets. can be translated into algebra:

Where
     x = # of rides on the bumper cars and 
     y = # of rides on the ferris wheel

     2x + 3y = 10 

Now the first part of our word problem is represented as a linear function. If we wanted, we could graph this function with the help of a table.  The line would represent all the solutions that work.

Next,

They went on 4 rides altogether.  Assuming the same variables x and y, we can place this equation underneath our original.

     2x +  3y = 10 
       x +   y = 4

These two formulas represent to linear functions that together make a system of equations.

Then, we can solve by any number of options:

• by graphing and identifying the point where the two lines cross

• by substituting
• x + y = 4 can be changed into x = y - 4
• we can then substitute the x in the first equation
• 2 (y - 4) + 3y = 10 and
• solve for y, then use our solution for y to help solve for x

• by multiplying and eliminating
• we can multiply the second equation by -3
• -3 (x + y = 4) becomes -3x + -3y = -12
• we can use that to eliminate the y in the first equation and
• solve for y, then use our solution for y to help solve for x

On Friday, we will have a quiz practicing these three options for solving.  I will find systems of equations, give you the answers to them and then ask you to show your understanding of all three of these processes for solving them.

Today we will practice the last two methods.

Please start with practicing substituting.  Watch the video of me solving #18 if  you need any help.

HW: pg 386 #18*, 19, 20

Then watch the videos of me solving #3 on page 401 and #17 on 402.  Take notes and then solve the remaining two by multiplying and eliminating.

HW: pg 401-2 #3*, 4, 5 and #17*, 18, 19

7.2 Substitution Review & 7.3 Elimination

Hope you all had a good weekend!

I corrected your quizzes and saw some consistent errors with regard to substitution.  One was that a number of people solved for variables in both equations and the other was a tendency to solve for y only rather than x.

It's important to note two things:

1. You can solve for either variable in either equation.  Generally, the best thing to do is to identify the variable that will be easiest to isolate.  
2. You only need to solve for one variable (of the four options) and substitute that into the other equation.  No matter which variable you choose, you will get the same answer.

For your classwork/homework please watch the videos below, take notes and then replicate the process of solving for all four variables for #2 (see HW below).

Substitution - pg 386 #15 - solve for first variable, first equation
Substitution - pg 386 #15 - solve for second variable, first equation
Substitution - pg 386 #15 - solve for first & second variables, second equation


HW: pg 386 #2 (solve for each variable in each equation, 4 times, same equation)

1. isolate x in 2x - 3y = 24, then substitute
2. isolate y in 2x - 3y = 24, then substitute
3. isolate x in 2x + y = 8, then substitute
4. isolate y in 2x + y = 8, then substitute

The answer for all of these should be x = 6 and y = -4

Then, for additional homework please:

1. make grids
2. translate the word problem into equations & 
3. solve by elimination

the following problems:

HW: pg 396 #43 & 45 (show grid, equations and solution by elimination)