section 2.4 buy, rent or lease?section 2.2 cc2015.notebook 3 march 30, 2015 when deciding whether to...

section 2.2 cc2015.notebook

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March 30, 2015

Section 2.4 Buy, Rent or Lease?

Asset – an item or a portion of an item owned, also known as property. Such as houses, vehicles, and land. Appreciation – increase in the value of an asset over timeDepreciation – decrease in the value of an asset over timeDisposable income – the amount of income that someone has available to spend after all regular expenses and taxes have been deducted.

Example : Vehicle Depreciation A new car that is bought for $25, 000 depreciates in value 25 % every year. What will be its resale value in 4 years after it is bought?

YearValue at start of year

Depreciation amount

Value at endof year


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March 30, 2015

A new RV Camper is bought for $39, 500 and it depreciates in value by 15% every year. What will be its resale value in 5 years after it is purchased?

A $80 000 tractor depreciates by 18 % each year. What is the resale value in 10 years?

A $385 000 house appreciates in value by 2.2 % each year. What is the price of the home in 6 years?

A $120 000 cottage appreciates in value by 3.4 % each year. What is the price of the home in 8 years?


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March 30, 2015

When deciding whether to rent, buy, or lease, each situation is unique. Since each situation is unique, it is impossible to generalize whether renting, leasing or buying is best. A cost benefit analysis should take everything into account.

Costs include the initial costs and fees, short term costs, long term costs, disposable income available, cost of financing, depreciation and appreciation, penalties for breaking contracts, and equity.

Benefits include convenience, comfort, safety, personal wants and

needs.

Appreciation and depreciation affect the value of a piece of property and should be considered when making decisions about renting, buying, or leasing.

Lease – A contract for purchasing the use of property, such as a building or vehicle, from another, the lessor, for a specified period.

If you lease something, you have no equity in the item.

Equity – The difference between the value of an item and the amount still owing on it. It can be thought of as the portion owned

Example: If a $25 000 down payment is made on a $230 000 home, $205 000 is sill owing and $25000 is the equity of portion owned.


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March 30, 2015

HOUSE

RENTING

• rental deposit on top of 1st month rent• monthly utilities• cable fees• limited access to laundry (usually in basement of building)• not responsible for maintenance, lawn mowing or snow removal

• pets sometimes not allowed.

BUYING

• legal fees• house inspection and water tests• property taxes• insurance• responsible for maintenance• building equity (ownership of property)• Can make changes • down payment


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March 30, 2015

CARLeasing legalling binding agreement sets out terms and conditions for using a new vehicle for a defined period (24, 36, or 48 months typically)

• pay for use of vehicle you don't own• at end of lease term, the car is returned to the dealer or you can purchase at an agreed upon price

• when you lease a car you only pay a portion of the car's value. In contrast, when you own a car, payments go directly to the total cost (price + interest)

• In short term, leasing will cost less than buying• the longer the term of the lease the higher the carrying cost and less attractive it becomes.

• if you intend to lease car for more than 3 years, better choice to buy.

• lease limits the number of km you can drive. Anything over this amount leads to stiff overcharges.

• If you terminate the lease before contracted date, you pay penalties.

• If involved in an accident or stolen, insurance pay out may not be enough to cover balance left on lease.

• required to follow maintenance schedule

Buying• ownership builds equity (you can sell in future).• can drive as many km.• make changes to car.


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March 30, 2015

Mary has been hired to complete at 16 week work term in White Rock, about 50 km from Vancouver. She is considering three options

• Rent a room in a bed and breakfast in White Rock for $400 per week. The cost would include all utilities and meals

• Lease an apartment in White Rock for $1200 per month. She must pay first and last months rent up front, plus a refundable damage deposit of $2000. She also needs to pay about 200 per month for all utilities

• Buy a used car for $12000 on credit, with regular monthly payments of $1000 and interest at 3.2 % compounded monthly. She would live in Vancouver with her parents for free and commute to White Rock daily. Driving costs such as gas, insurance, and maintenance would be about $250 per week. The car will depreciate by 20 % each year

Which option would you advise Mary to choose?


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March 30, 2015

Example:

1. Tom is considering buying a lawn mower. He can hire someone to cut his grass for $50 per cut. He can buy a new tractor for $2200 or he can buy the same lawn tractor used for 70% of the purchase price (2 years old). Tom cuts his grass on average 20 times per year. Which option is best? Explain. (Forget gas and maintenance costs)

2. Heather bought a house for $195 000. She negotiated a mortgage of 80% of the purchase price of the home. What is the value of the mortgage?

3. Heather is putting a 20 % down payment on her house she bought in the question above. What is the value of the down payment.

4. Grant bought a boat for $8950. A 5% down payment is required. What is the value of the down payment?


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March 30, 2015

Attachments

Martensmath.docx

Chapter 8 Assignment 1.docx



Independent Study ANS.pdf

Independent Study Booklet.docx

Martensmath

8.1

https://www.youtube.com/watch?v=bwkA8IJcmVg

https://www.youtube.com/watch?v=jFV0Q-TA9J8

8.2

https://www.youtube.com/watch?v=c9tbY3uYLGE

https://www.youtube.com/watch?v=qJtUsPjCyDg

8.3 & 8.5

https://www.youtube.com/watch?v=IRIDZA0jI5k

https://www.youtube.com/watch?v=V3JazrgNdOI

https://www.youtube.com/watch?v=9idDOwXyNCc

8.4

https://www.youtube.com/watch?v=PfGSnXRDRTQ

https://www.youtube.com/watch?v=ucXmXvPO6AQ

https://www.youtube.com/watch?v=bwkA8IJcmVg

8.6

https://www.youtube.com/watch?v=6dpecxq27YI

https://www.youtube.com/watch?v=6NhMxrrlhTs

https://www.youtube.com/watch?v=NXpzsOtHtJQ

https://www.youtube.com/watch?v=fmb9KFa_cH4

SMART Notebook

Chapter 8 Assignment #1Name______________________Section 8.1 and 8.2Due Date: February 27, 2015

1. Calculate the unit rate of each product. Round off each answer to the nearest cent.

a. $1.99 for 12 pencils

b. $3.98 for 6 bottles of pop

2. A 20-ounce bag of popcorn costs $2.80. If the unit rate stays the same, how much does a 35-ounce bag cost?

3. Mr. Scrub offers three ways to pay for car washes: a book of six car wash coupons for $33, a special offer of two washes for $11.50, or one wash for $5.95. Which option offers the least expensive unit rate for one car wash?

4. If a type of salami at the deli costs $1.39 per 100g, how much will you pay for 350g?

5. As a custodian, Janine makes a cleaning solution by mixing 30g of concentrated powdered cleanser into 2 L of water. At the same rate, how much powder will she need for 5 L of water?

6. An office has decided to track how much paper it uses to reduce waste. At the end of each month, the secretary records the total number of sheets used and their weight. If paper weighs 10.8 lb for every 500 sheets, how much will 700 sheets weigh?

7. John runs at a rate of 10 km/h. When he runs at this rate for 2 h, he burns 760 calories. Loretta runs at a slower rate, 8 km/h, and burns 150 calories in 30 minutes. How much longer would Loretta have to run on order to burn the same amount of calories as John?

8. The low temperature in Summerside for a certain day was 9˚C, at 4:30 am. The temperature then rose steadily at a constant rate until the high temperature of 25.5˚C was recorded at 3:30 pm. A weather forecaster predicted that the temperature would increase at the same rate for the next day, from a low of 11˚C at 4:00 am. At that rate, what will the temperature be at 1:00 pm on the next day?

SMART Notebook

Chapter 8 Assignment #2Name______________________Section 8.3 and 8.4Due Date: March 13, 2015

1. An actual laptop has a width of 42 cm. Determine the scale factor used for the image of the laptop.

2. A driving distance is 600 km. The distance shown on a map is 4 cm. What is the scale factor? Express the answer as a fraction.

3. Use similar triangles to find the height of the tree.

4. Explain how you could determine if Figure B is an accurate enlargement of Figure A?

5. Andy and Ben each ordered a pizza at Pizza Delight. Andy ordered a 6-inch diameter pizza and Ben ordered a 12-inch diameter pizza. How many times larger was the area of Ben’s pizza than Andy’s pizza?

6. When making a photocopy of a 10 cm by 15 cm photograph, Elizabeth enlarged the picture by a scale factor of 150%. By what percent was the area of the photograph enlarged?

7. The scale between two similar rectangles is 1:3. The length of the smaller rectangle is 3 cm longer than its width. The sum of the perimeters of both rectangles is 110 cm. What are the dimensions of the larger rectangle?

SMART Notebook

Chapter 8 Assignment #3Name______________________Section 8.5 and 8.6Due Date: April 3, 2015

1. A standard indoor volleyball has a diameter of 8.3 in. A standard basketball has a diameter of 9.6 in. Determine the scale factor that relates a standard indoor volleyball to a standard basketball. Round off the answer to the nearest hundredth.

2. A triangle with an area of 15 cm2 has been enlarged by a scale factor 3. How many times larger is the new triangle? What is its area?

3. The area of a circle is 20 in2. A similar circle is 5 in2. What scale factor was used to make the reduction?

4. A 1:20 scale model of a boat has a length of 20mm and a height of 14mm. What are the dimensions of the boat to the nearest tenth of a metre?

5. The surface area of a rectangular prism is 5.5 times larger than that of the original rectangular prism. How many times greater is the volume of the larger rectangular prism?

6. The dimensions of the largest nesting doll are exactly 4 times larger than the corresponding dimensions of the smallest nesting doll.

a. How many times greater will the surface area of the largest doll be than the smallest doll?

b. How many times greater will the volume of the largest doll be than the smallest doll?

SMART Notebook

SMART Notebook

Chapter 8: Proportional ReasoningName______________________Math 521A: Independent Study Booklet

8.1 Comparing and Interpreting Rates

Learning Goals:

1. Demonstrate understanding of new terminology pertaining to rates.

2. Convert quantities from one unit of measurement to a different unit of measurement.

3. Calculate unit rates.

4. Compare unit rates to determine the better deal.

Terminology:

Rate:a comparison of two amounts that are measured in different units

Example: Typing 240 words/8 minutes

Unit Rate:a rate in which the numerical value of the second term is 1

Example: Typing 240 words in 8 minutes would have a unit rate of 30 words/minute

Example Problems:

1. A 12-pound turkey costs $22.50. What is the unit rate to the nearest penny?

You try:

Ian is training to run a half-marathon, which is 21.1km. He can run this distance in 2.2 hours. What is his speed in kilometres per hour? Answer to the nearest tenth.

2. Orange juice is sold in 1.5L cartons and 250 mL boxes. A 1.5 L carton sells for #3.75 and ten 250 mL boxes sell for $7.39. Which size costs less per millilitre?

3. Fuel efficiency in Canada is reported in L/100 km (how many litres it takes to travel 100 km). The lower the top number, the better fuel efficiency the vehicle has. Jasmine drove for 510 km and used 46.7 L of gas. What is her car’s fuel efficiency to the nearest hundredth?

You Try:

Jake’s car will get 875 km using 55.3 L of gas. Amanda’s car will get 515 km using 33.7 L of gas. Whose car has better fuel efficiency?

4. A 5kg bay of potatoes cost $8.15. A 10lb bag of potatoes costs $7.10. Which is a better buy for the consumer?

You Try:

A peregrine falcon can fly at a top speed of 16 km in 3 min. A cheetah can run at a top speed of 112 km/h. Which animal can travel faster?

Questions to try: p. 458-459: # 1, 2, 4, 5, 6, 7, 8, 9

8.2 Solving Problems that Involve Rates

Learning Goals:

1. Solve problems using unit rate and proportion.

Terminology:

Proportion: involves two equivalent ratios, where both numerators in the proportion must have the same unit, and both denominators must have the same unit.

To solve a proportion you must set up your problem as equivalent fractions. Knowing three of the four pieces of information you will be able to solve for the fourth.

Example Problems:

1. A screw has 64 turns over a distance of 50mm of thread. Determine the number of turns on a screw with the same pattern over 40mm of thread. Round your answer to the nearest number of turns.

2. A dosage of an antibiotic for a person with a mass of 85 kg is 15 mL. What dosage of antibiotic is needed for a person whose mass is 65 kg? State the dosage to the nearest tenth of a mL.

You Try:

17 kg of Yukon Gold potatoes costs $26.80. Determine the cost of 5kg of potatoes. Round your answer to the nearest cent.

3. Paula is asked to order snacks for an office meeting of 180 people. She decides to order dessert squares, which come in boxes of 24. She estimates that she will need 2.5 squares/person. How many boxes should she buy?

You Try:

Michael must order snacks for an office meeting of 170 people. He decides to order tarts, which com in boxes of 12. He estimates that he will need 1.5 tarts per person. How many boxes should Michael buy?

4. Jenna wants to defrost a frozen turkey in her microwave. The turkey has a mass of 4.23 kg. A cookbook says it will take 21 minutes to defrost 3 lb of meat. How long, to the nearest minute, should Jenna set the timer on defrost for?

You Try:

If 15 kg of beef costs $127.00, how much will it cost, to the nearest penny, for 25 lb of beef?

5. Bob burns 620 calories in a Cardio Kickboxing class which lasts for 2 hours and 120 calories in a Body-Sculpt class that lasts for 30 minutes. If he does Cardio Kickboxing for 3 hours, how many calories would he burn? How much longer would he have to do Body-Sculpt to burn the same number of calories?

Questions to Try: p. 466-468: # 1-4, 7-11, 15

(Complete Assignment #1Due Date: February 27, 2015)

8.3 Scale Diagrams

Learning Goals:

1. Calculate scale factor

2. Use scale factors to solve problems.

3. Use scale factors to draw scale diagrams.

Terminology:

Scale diagram:A drawing in which measurements are proportionally reduced or enlarged from actual measurements; a scale diagram is similar to the original.

Scale: The ratio of a measurement on a diagram to the corresponding distance measured on the actual object. The l measurement is always written second. A scale always includes units, and they do not necessarily have to be the same.

Scale factor:A number created from the ratio of any two corresponding measurements of two similar shapes or objects. Scale factor can be written as a fraction, decimal, or percent. The actual measurement is always on the bottom of the fraction. The scale factor does not include units, because they are assumed to be the same.

Scale is represented by k.

If a scale factor is:

Less than 1 the diagram is smaller than the actual object being represented

Greater than 1 the diagram is larger than the actual object being represented

Examples:

1. Determine the scale factor that was used to transform rectangle A into rectangle B.

2. A desk that is 150 cm long is drawn in a scale diagram as 15 cm long. What scale factor was used in the diagram?

3. A floor plan of a house was created using a scale of 2 cm: 1 m. What scale factor was used?

4. A scale drawing uses a scale factor of . Is the drawing a reduction or an enlargement? If the length of the object in the drawing is 5 cm, what is the length of the actual object?

You Try:

A scale diagram of an animal cell has a diameter of 3.5 cm. The actual cell has a diameter of 0.25 mm. What scale factor was used to create the diagram? Is this a reduction or enlargement?

5. An 8 x 10 inch photograph is going to be used to create a display poster. The maximum allowable poster dimensions are 30 x 40 inches. What is the greatest scale factor that could be used to enlarge the original photo and still fit the maximum dimensions? What would the poster dimensions be after this enlargement?

6. To make a scale drawing of a rectangular park, a scale factor of or 0.001 is to be used. If the lenth and width of the park are 100 m and 75 m, how long would the length and width be in the scale drawing?

7. A driving distance is 250 km. The distance shown on a map is 5cm. What is the scale factor?

Questions to Try: p. 479-482, # 1-4, 6, 7, 11-15

8.4 Scale Factors and Areas of 2-D Shapes

Learning Goals:

1. Demonstrate understanding of how the areas of similar shapes are related by their scale factor.

2. Calculate a scale factor using measurements from similar shapes.


Key Ideas:

When a 2-D shape undergoes an enlargement or reduction by a scale factor, k, the resulting shape is similar to the original shape.

If two 2-D shapes are similar and their dimensions are related by a scale factor, k, then the relationship between the area of the similar shape and the area of the original shape can be expressed as:

Area of Similar 2D shape = k2 x (Area of Original Shape)

This formula can be rearranged to determine the scale factor if you know the areas of the two shapes.

Examples:

1. A 3 cm x 5 cm rectangle has been enlarged by a scale factor of 2 to create a similar rectangle. How are their areas related?

2. A triangle whose area is 76 cm2 will be reduced by a scale factor of . Determine the area of the reduced triangle to the nearest square centimetre.

You Try:

A circle of area 10 cm2 will be enlarged by a scale factor of 5. Determine the area of the enlarged circle.

3. The area of a parallelogram is 900 mm2. The area of a smaller, similar parallelogram is 100 mm2. What scale factor was used to make this reduction?

You Try:

A trapezoid was reduced from an area of 750 mm2 to 30 mm2. What scale factor was used to make this reduction?

4. Jasmine is making a kite from a 2:25 scale diagram. The area of the scale diagram is 20 cm2. How much fabric will she need for her kite?

You Try:

Suppose Jasmine’s scale diagram for the kite had been drawn using a ratio of 1:20, and the area of the scale diagram had been 30 cm2. How much fabric would Jasmine have needed for her kite?

5. A computer screen measures 35 cm by 55 cm. An image on the computer is projected onto a whiteboard with a screen area of 7238 cm2. Determine the length and width of the whiteboard to the nearest cm.

(Complete Assignment #2Due Date: March 13, 2015)Questions to Try: p. 487-489, # 1-3, 6, 7, 9, 10, 13, 14

8.5 Similar Objects: Scale Models and Scale Diagrams

Learning Goals:

1. Calculate a scale factor.


Key Ideas:

Just as in the case of 2-D objects, you can determine if 3-D objects are similar by checking to see if teh scale factor holds try for each measurement of the object.

The scale factor, k, can be found using this formula:

As in the last section, the actual measurement is on the bottom of the fraction.

Examples:

1. A 1:18 scale model of a car has a length of 206.3 mm, a width of 94.5 mm and a height of 78.2 mm. What are the dimensions of the actual car to the nearest tenth of a metre?

You Try:

A 1:25 scale model of a tractor trailer is 0.4 ft tall, 0.3 ft wide, and 1.5 ft long. What are the dimensions of the actual trailer?

2. Which of the following rectangles is similar to a rectangle 80 cm long, 45 cm wide, and 30 cm high?

A rectangle that is 20 cm long, 15 cm wide, 10 cm high



You try:

Which of these cylinders is similar to a cylinder 10 cm long and 25 cm in diameter?

A cylinder 16 cm long and 40 cm in diameter

A cylinder 4 cm long and 1.5 cm in diameter

A cylinder 12 cm long and 3.5 cm in diameter

3. A sculptor wishes to reproduce a statue that is 7ft 4in tall as a scale model which is 16 in tall. What scale factor would the sculptor use?

Questions to Try: p. 497-500, # 1-5, 8, 9, 11

8.6 Scale Factors and 3-D Objects

Learning Goals:

1. Calculate scale factor.

2. Use scale factor to solve problems involving volume and 3-D objects.

Key Ideas:

Just as the areas of similar objects are related so are the volumes of similar 3-D objects.

Recall:

So....

So, if you know the dimensions of a scale diagram or model of a 3-D object, as well as the scale factor, you can determine the surface area and volume of the actual object, without determining the dimensions!

Examples:

1. A cube is a 3-D shape that is always similar to other cubes. If one cube has an edge length of 1.5 cm and another cube has an edge length of 6.0 cm,

a. What scale factor is needed to enlarge the small cube to the larger one?

b. How many times greater will the surface area of the larger cube be?

c. How many times greater will the volume of the larger cube be?

You Try:

A stage director needs a large chess bishop for a scene. The bishop in her chess set is 78 mm tall. She wants the enlarged bishop to be 1.56 m tall.

a) What scale factor must she apply to create the enlarged bishop

b) How many times greater will the surface area of the larger bishop be?

c) How many times greater will the volume of the larger bishop be?

2. An orange has a diameter of 7 cm. A grapefruit has a diameter of 12 cm. How many times greater is the volume of the grapefruit than that of an orange?

3. The surface area of an enlarged triangular prism is 6.25 times greater than that of the original prism. How many times greater is the volume of the enlarged prism than the volume of the original?

You Try:

If the surface area of an enlarged cylinder is 64 times greater than that of the original cylinder, how many times greater is the volume?

4. A cook has a set of four mixing bowls. The bowls stack inside each other and are similar. The two largest diameters are 30 cm and 28 cm. The scale factor is the same form each bowl to the next smaller bowl. What are the diameters of the two smallest bowls to the nearest tenth of a centimetre?

Questions to Try: p. 508-510, # 1-4, 6, 8, 9, 13

(Complete Assignment #3Due Date: April 3, 2015)

SMART Notebook

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