Math 8 with Mr. Hobart - Week 11 Learning Opportunity.

Below is a fictional scenario about a woman named Janice who has bought tickets in a charity lottery. Questions are provided at the end of the document. This task will be difficult for students who have trouble with word problems. Please do not hesitate to email me questions or ask for guidance. Don’t stare at the question not understanding for 30 minutes. Instead shoot me off an email! There is a lot of information given about the scenario. It is your job to be able to look at each question being asked and determine which information will be relevant to that question while answering it.

Janice and her Lottery Dream

A charity is hosting a lottery and Janice decides to purchase three tickets at a cost of $1248.99. The prize for the lottery is partly cash, $20 000, but also includes a brand new house on a property of the winner’s choice (from a given selection). The winner of the lottery will get to choose from three different houses as part of their prize. See appendix A to view the three properties with dimensions that are available for selection by the winner of the lottery. See appendix B for the dimensions of the houses on these properties. The lottery will be drawn after $750 000 worth of tickets have been sold.

Some of Janice’s friends have also bought tickets in the lottery. Chandler bought twice as many tickets as Ross, Joey bought 2 fewer than Chandler and Monica bought twice as many Joey. Together Janice and her friends purchased 24 tickets.

Janice is a dreamer. As she dreams about winning, she thinks about what is important to her in a house. Janice wants a big house. A lot of people look at floor space as being really important for determining how big a house is. Janice is a little bit different though because she values high ceilings just as much as floor space. Therefore, instead of just floors pace, the best house for Janice would be the one with the greatest volume.

Janice likes to garden. If she were to win, she would also want a property with a large area so that she could do as much gardening as possible. She figures that if she planted her favorite seeds in her garden on the first day she arrived at the house, it would take 5 days for the seeds to sprout. Then every second day afterwards, the sprouted seeds would grow an inch.

In order to grow with the seeds though, Janice will need to ensure her raised garden beds are in place right away and full of something to grow in. Her raised garden beds are built as rectangles into the ground (see appendix C for a visual example of what one of her garden beds looks like). Typically she measures her garden beds in feet. Her raised garden beds mesure 4ft by 8ft with a height of 2ft. The wood she has is 1/10 of a ft. thick. She has 5 raised garden beds she would bring to the house immediately if she won to plant her seeds in. Janice also noticed recently that her garden beds are in terrible need of a paint job.

Depending on what she is growing, Janice fills her garden beds to different heights. Usually she fills 3 garden beds 2/3 full and 2 raised garden beds 3/4 full. The way that Janice fills her garden beds is by creating a balanced soil mixture. She typically mixes equally sized bags of compost, peat and some cheap topsoil together to create an organic mixture that her plants love. Usually she mixes in 32 bags of compost, 24 bags of peat and 24 bags of the cheap top soil and that is enough to fill one of her garden beds 3/4 full.

Thankfully Janice has a wholesaler soil distributor she is friends with and gets her soil materials at a significant discount. If her dream of winning actually came true, she would not be able to bring the old soil from her current house. Instead she would need to purchase new soil. To do this she would go to her wholesaler friend who normally charges $3 for a bag of compost, $6 for a bag of peat, and $5 for a bag of topsoil. Janice would get a 95% discount on her purchase because she is friends with the wholesaler making things much more affordable for her.

Finally, Janice feels like it might be a good idea to invest the money she would win to invest in a company she and her friend George were thinking of starting a company called Vandalay Industries. Without getting into too much detail about what this company would actually do, Janice feels like after one year she would earn 6.5% interest after 1 year on her investment which would be great! However, before she invested the rest of her winnings, Janice would need to pay a few bills with the cash portion of the prize. She currently owes $2300 to Visa after buying her tickets to the lottery.

Wish Janice and her friends luck in the lottery!

Questions:

1. Janice likes to garden. If she were to win, she would want a property with a large area so that she could do as much gardening as possible. Which property has the greatest area? Show all your work to prove your answer. Note that the house size does not need to be accounted for.

2. What is the unit price per lottery ticket for this charity’s lottery?

3. How many tickets need to be sold before the lottery is drawn?

4. What is the probability that Janice will win the charity lottery (give answer as a fraction and a percent)?

5. Create an algebraic equation that demonstrates this scenario:

Some of Janice’s friends have also bought tickets to the lottery. Chandler bought twice as many tickets as Ross, Joey bought 2 fewer than Chandler and Monica bought twice as many Joey. Together Janice and her friends purchased 24 tickets.

Solve the equation and note how many tickets each person bought (I want to see an algebraic equation even if you solve it in a different way).

6. How much did Janice and her friends altogether spend on the lottery?

7. What is the mean, median, and mode of number of tickets purchased by Janice and her friends?

8. Janice wants her house to be as big as possible and looks at volume instead of floor space to determine size. Which house would give her the greatest volume?

9. Create a linear equation in the form y = mx + b that describes the following:

Janice figures that if she planted her favorite seeds in her garden on the first day she arrived at the house, it would take 5 days for the seeds to sprout. Then every second day afterwards, the sprouted seeds would grow an inch.

State the domain and range

(Note that you can assume that the seeds after sprouting will continue to grow forever but you cannot grow into negative days or negative heights of sprouts. This is a very difficult question)

10. If one of Janice’s raised garden beds was completely full of soil, what would the volume of that raised garden bed be?

11. If one of Janice’s raised garden beds was completely full of soil, what would the volume of that raised garden bed be not including the wood?

12. Janice needs to paint her garden boxes. She only paints the outer faces of the garden boxes and not the inside, top or bottom. Determine the surface area of paintable areas of her 5 garden boxes to help her predict how much paint she will need.

13. We know how much soil Janice usually fills her 5 raised garden beds with. 3 garden beds are filled 2/3 of the way up and 2 raised garden beds are filled 3/4 full. If Janice took the amount of soil she normally buys for the 5 garden beds, and then started filling her garden beds full instead of to the amount she would normally, how many garden beds could she fill? Give your answer in mixed number form.

14. What is the ratio of Janice’s soil mixture (reduced)?

15. How much does it cost Janice to fill one raised garden bed 3/4 full of her soil mixture?

16. How much does it cost Janice to fill all of her 5 raised garden beds to the heights she prefers?

17. If Janice won the lottery, paid off her debt to Visa, and then invested the rest of the money in Vandalay Industries, assuming she is right about the rate of return, how much money would Janice receive as profit on her investment after one year?

18. What is the perimeter of each property?

19. In your opinion, if she won, which property should she choose based on her needs? Explain, with evidence to support your position, why you selected the property you did.

20. In your opinion, was it a good idea for Janice to buy these lottery tickets? Explain your position.

Appendix A

Appendix B

Note that unless otherwise stated, all rooms are rectangular prisms.

House on property 1

Main level (all rooms have 3m ceilings)Master bedroom 3.35m by 4.26mBedroom 2.43m by 4.26mFull bathroom (cylinder) Diameter of 2.5 metersSunroom 3.35m by 1.82mDining room 2.43m by 3.04mFoyer 2.43m by 1.82mKitchen 2.43m by 5.18mLiving room 5.48m by 3.35m

House on property 2

Main level (all rooms have 3.5m ceilings)Kitchen 2.66m by 3.07mDining room 2.36m by 2.31mLiving room 4.74m by 4.01mFull bathroom 2.31m by 2.28mMaster bedroom 3.60m by 3.25mBedroom 3.04m by 3.04mLaundry room (triangular prism) 2.36m by 0.81m

House on property 3

Main level (all rooms have 3.5m ceilings)Master bedroom 3.35m by 4.26mBedroom 2.43m by 4.26mFull bathroom (cylinder) Diameter of 2.75 metersDining room 2.43m by 3.04mFoyer 2.43m by 1.82mKitchen 2.43m by 5.18mLiving room 5.48m by 3.35m

Appendix C

Appendix D

BONUS QUESTION

1. Imagine that you had one of Janice’s raised garden beds filled appropriately with really nutrient rich soil and wanted to plant a vegetable garden. What would you plant in it? Research your seed and sprout selections from https://www.westcoastseeds.com/ (hover your mouse over ‘shop’ and then select ‘vegetable seeds’). Be sure to take into account the size of the box (same size as Janice’s), our local climate, the time of year it is, and spacing instructions when planning out your raised garden bed. Write a short description of your plans for the raised garden bed and then sketch a top down view model of what will be planted (I don’t want you to draw the vegetables but instead label in your model where you would plant them). Although it doesn’t need to show every detail, be sure to include some dimensions (space between rows, between seeds planted, etc.). Be sure to include various kinds of crops to avoid pest problems common in monoculture gardens. For an example of something similar to the model you are looking to create see appendix D (although on yours you will have more specific seed types and potentially fewer drawings).