Muscle Mania and Healthy Heart Gym

Transcription

1 Muscle Mania and Healthy Heart Gym Allie Algebra and her friend Carly Coefficient wanted to get in shape. Allie Algebra joined the Muscle Mania Gym. To get a membership to the Muscle Mania Gym she had to pay a $100 initial sign-up fee plus $30 per month. Carly Coefficient joined the Healthy Heart Gym. She had no initial sign up fee, but had to pay $40 per month. How long did it take for both Allie and Carly s total costs on gym memberships to be the same? I. Variable Let represent. II. Expressions The total cost for Muscle Mania Gym +. after an unknown # of months Write this expression using numbers and variables: The total cost for Healthy Heart Gym +. = after an unknown # of months Write this expression using numbers and variables: III. Equation: When will the total costs of Muscle Mania Gym and Healthy Heart Gym be the same? Write an equation to represent this: IV. Solve the Equation: V. How long did it take for Allie and Carly s total cost on gym memberships to be the same?

2 Fill in the chart below: # of Months x Muscle Mania Gym Healthy Heart Gym VI. Graph each gym membership on the coordinate plane below 520 Cost (in dollars) # of Months

3 Allie and Carly s $$$$ Allie Algebra currently has $60 saved up. She earns $20 a week babysitting. Carly Coefficient does not work. She loves to go shopping. Luckily, she has $300 saved up, but she spends $40 a week at the mall. How many weeks will it take before Allie and Carly have the same amount of money? I. Variable Let represent. II. Expressions Amount of money Allie has after. +. an unknown # of weeks: Write this expression using numbers and variables: Amount of money Carly has after an unknown # of weeks: Write this expression using numbers and variables: III. Equation: When will the total saving of Allie and Carly be the same? Write an equation to represent this: IV. Solve the Equation: V. How long did it take for Allie and Carly s total savings to be the same?

4 Fill in the chart below: # of Weeks x Allie s $$$ Carly s $$$ VI. Graph each Allie and Carly s $ balance on the coordinate plane below 390 Amount of Money (in $) # of Weeks

5 Word Problem Name You already have $20 saved up. You earn $12 a week babysitting. Your friend has $100, but spends $8 a week. When will you and your friend have the same amount of money? 1. Complete the table below for each person. Week Your $ Friend s $ 2. Graph each plan on the coordinate grid below: Money (in dollars) Weeks

6 3. Choose the equation that would determine how many weeks (w) it would take for you and your friend to have the same amount of money: a w = w b w = 100 8w c w = 100-8w d w = 8w Next, solve the equation you have chosen. Look at where the two graphs cross on the front page. The number of weeks where the graphs cross should "agree" with your solution above. If these are not the same, find and correct your answer(s).

7 Extra Practice Problems for on board (if time) A customer is trying to decide which cell phone plan to use. Plan A costs $35 a month plus $4 per hour. Plan B costs $45 per month plus $2 per hour. How many hours does it take for the monthly cost for each phone plan to be the same? A company president is buying his whole company a key chain. If he buys from Keychains R Us, there is a $120 design fee, plus $3 per keychain. If he buys from Keychains Unlimited, there is no design fee, but each keychain costs $6. For how many keychains would the total cost for each company be the same? A hairdresser is considering ordering a certain shampoo. Company A charges $5 per 8-oz bottle plus a $10 handling fee per order. Company B charges $1 per 8-oz bottle plus a $30 handling fee per order. For how many shampoo bottles would the cost of each company be the same? At Sport Chalet, you can rent a camping tent for an initial fee of $20 plus $10 per day. At REI, the cost is an initial fee of $15 plus $12 per day.

8 Homework # Name Word Problems (involving variables on both sides of the equation) 1. Verizon charges a $31 monthly fee plus 20 cents per additional minute. AT&T charges a $25 monthly fee plus 50cents per additional minute. After how many minutes is the cost for each cell phone company the same? 2. Corepower Yoga has no initial sign up fee, but has a monthly membership fee of $110. YogaWork has an initial sign up fee of $120 and a montly membership fee of $70. After how many months is the total cost for a yoga membership the same? 3. Your teacher is looking into buying a class set of calculators online. Company A charges a $20 shipping fee, plus $7 per calculator. Company B charges a $10 shipping fee, plus $8 per calculator. For how many calculators would the total cost for each company be equal? 4. You have $500 in savings and save an additional $10 each week. Your friend has $700 in savings, but spends $15 a week. After how many weeks will you and your friend have the same amount of money?

9 5. You buy a cactus that is 1 foot tall, and grows 2 feet per year. At the same time, you buy a rose bush that is 3 feet tall and grows 1 foot per year. After how many years will the cactus and the rose bush be the same height? 6. To rent a paddle board, there is a daily fee of $10, plus an hourly fee of $8. To rent a kayak, there is a daily fee of $6, plus an hourly fee of $10. After how many hours will the cost for each rental be the same? 7. A job at a bookstore offers to pay you $11 per hour. A job at a yogurt shop offers to give you a $150 bonus for starting work, and $8 per hour. After how many hours would your money earned at the bookstore be the same as at the yogurt shop. 8. You are looking into purchasing a car. The SUV costs about $20,000 and has a monthly maintenance/gas fee of about $400. The hybrid vehicle costs about $24,000 and has a monthly maintenance/gas fee of about $200. After how many months will it take for it to be a better value to buy the hybrid?