1. Problem: Nathan pays $68 for his favorite x-box game. Each month he has to pay $3 to clean the game since he plays it so much. If he doesn’t pay for cleaning Captain Crusader doesn’t show up clearly on the screen and that is so annoying to him. Bryan pays $93 for his favorite x-box game but only pays $2 a month for cleaning since his mom works at the game store and gets a discount on cleanings. How many months will it take for Bryan to pay less than Nathan? When you’re done with this lesson you should be able to use linear equations to solve real world problems! You’ll gain valuable skills that include: organizing information, writing linear equations, and using those equations to calculate in the real world. Click here to get started!

2. Highlight important information and cross out unnecesary information. Group information based on their units. Step 1Step 2 Nathan pays $68 for his favorite x-box game. Each month he has to pay $3 to clean the game since he plays it so much. If he doesn’t pay for cleaning Captain Crusader doesn’t show up clearly on the screen and that is so annoying to him. Bryan pays $93 for his favorite x-box game but only pays $2 a month for cleaning since his mom works at the game store and gets a discount on cleanings. How many months will it take for Bryan to pay less than Nathan? Click on each step to learn how to organize information. Nathan pays $68 for his favorite x-box game. Each month he has to pay $3 to clean the game since he plays it so much. If he doesn’t pay for cleaning Captain Crusader doesn’t show up clearly on the screen and that is so annoying to him. Bryan pays $93 for his favorite x-box game but only pays $2 a month for cleaning since his mom works at the game store and gets a discount on cleanings. How many months will it take for Bryan to pay less than Nathan?

3. Look at the table of information and notice that the one time fee of the game cost represents the y-intercept or the “b” of the linear equation. Now let’s take this problem and use it to set up linear equation : Nathan pays $68 for his favorite x-box game. Each month he has to pay $3 to clean the game since he plays it so much. If he doesn’t pay for cleaning Captain Crusader doesn’t show up clearly on the screen and that is so annoying to him. Bryan pays $93 for his favorite x-box game but only pays $2 a month for cleaning since his mom works at the game store and gets a discount on cleanings. How many months will it take for Bryan to pay less than Nathan? Step 1Step 2 Click on each step to learn how to set up equations. Look at the table of information and notice that the monthly fee of the cleaning cost represents the slope or the “m” of the linear equation. Nathan: y=3x+68 Y=mx+b Bryan: y=2x+93

4. Solve the system of equations to figure out how many months it will take for the payments to be equal. Conclude that Bryan will pay less than Nathan after 26 months. Step 1Step 2 Nathan pays $68 for his favorite x-box game. Each month he has to pay $3 to clean the game since he plays it so much. If he doesn’t pay for cleaning Captain Crusader doesn’t show up clearly on the screen and that is so annoying to him. Bryan pays $93 for his favorite x-box game but only pays $2 a month for cleaning since his mom works at the game store and gets a discount on cleanings. How many months will it take for Bryan to pay less than Nathan? Click on each step to learn how to use the equations to solve the problem. Substitute “3x+68” for “y” in “y=2x+93” to get “3x+68 = 2x+93” Now solve for “x” by subtracting “2x” and “68” from both sides of the equation. This gives you “x=25” This means that after 25 months Nathan and Bryan will pay the same fee.

5. Now Let’s Practice! Don’t forget: When using linear equations to solve real world problems you must first learn to identify the slope and the y-intercept of the situation. The slope is always a rate and you should recognize that it occurs often (ex. monthly, daily, per…, each…, every…, etc.). The y-intercept represents a one time fee or a fixed rate (ex. down payment). Then you plug these values into the slope-intercept form of the equation of a line “y=mx+b”. After you’ve done this you can then solve the problem by plugging in the “x” or “y” value given.

6. Writing a Linear Equation Write a linear equation to model the following situations: – Jeremy buys an iPod for a down payment of $25 and a $10 monthly payment. – Lidia pays $35 to get acrylic nails put on and then pays $15 per month to get them filled. – Derek gets paid a salary of $1,300 plus $20 a night in tips. Identify the slope (“m”) Plug in the “m” and “b” to y=mx+b Identify the y-intercept (“b”) Click on the tasks to write a linear equation.

7. Writing a System of Linear Equations Write a system of linear equations for the following examples: – Luis and Eddie are buying new light systems to decorate their cars. Eddie finds one that costs $39.99 and requires new batteries that cost $4.99 each month. Luis finds one that costs $49.99 and requires new batteries that cost $3.99 each month. – Nancy and Diana sell balloons for special occasions. The Happy Birthday package costs $12.50 plus $0.75 per candy bar. The Get Well package costs $9.70 plus $0.50 per piece of candy. Identify the slope (“m”) Plug in the “m” and “b” to y=mx+b Identify the y-intercept (“b”) Click on the tasks to write a system of linear equations. Eddie: y=4.99x + 39.99 Luis: y=3.99x + 49.99 Birthday: y=.75x + 12.50Get Well: y=.50x + 9.70

8. Using a System of Linear Equations to Solve Problems Write a system of linear equations to solve the following problem: – Brenda and Moises decide to buy a new car and they need to figure out which dealership will give them the best deal. Xela Cars offers them a down payment price of $500 and a monthly fee of $299 for 48 months. While Guatemala Driving Solutions offers a down payment of $400 and a monthly fee of $307 for 45 months. Which dealership should they buy their car from? Identify the slope (“m”) Plug in the “m” and “b” to y=mx+b Identify the y-intercept (“b”) Click on the tasks to write a system of linear equations. Plug in the “x” to y=mx+b Identify the independent variable (“x”) Xela Cars y = 299x + 500Guatemala Driving Solutions y = 307 x + 400 Xela Cars 14,852 = 299(48) + 500 Guatemala Driving Solutions 14,215= 307(45) + 400 Identify the solution.

9. Yay Hooray!!! You can now use linear equations to solve real world problems. Brenda and Moises thank you for helping them find the most affordable car!!!

10. Jasmine is trying to find the cell phone plan that will work best for her. Her parents say she talks too much on the phone and tell her she cannot get a plan with more than 500 minutes. They also tell her that they’ll pay for the plan but that she has to pay for the minutes she goes over. She looks up on the internet and finds out that AT&T and Verizon offer a plan of 450 minutes per month for $39.99 while T Mobile offers a plan of 500 minutes per month for $39.99. AT&T charges a fee of $.21per minute for every minute you go over your allotted amount. Verizon charges a fee of $.23 per minute for every minute you go over your allotted amount. As a favor to their customers, Verizon shuts off the phone if the customer goes more than 100 minutes over their plan. T Mobile charges $.37 per minute for every minute you go over your allotted amount of minutes. If Jasmine usually talks on the phone for 650 minutes each month, which plan would be cheapest for her? Make sure you use a linear equation for each phone company to help Jasmine compare her rates.

11. Organize the information given: Write equations based on total cost and minutes used over the amount alloted by the plan. Step 1Step 2 Jasmine has a lot of information to sort through. Let’s use Algebra to help her find the best phone plan. Step 3 Now conclude that Verizon is the best deal for Jasmine.

12. Now get going….go on….start solving your own problem…….!