Constant of Proportionality/Proportional Relationships

Better Buy

100

Staples is having a sale on pencils.  A pack of 30 sells for $8 and a 12-pack costs $5.  Which one is the better buy?

30 pack = $0.27

12 pack = $0.42

200

Tops sells chicken at a cost of $8.35 for 5 lbs. Walmart sells chicken at a cost of $13.60 for 8 lbs. Which one is the better buy?

Tops = $1.67

Walmart = $1.70

300

Tom drove 290 miles and used 23.2 gallons of gas.  His sister Ann drove 225 and used 15 gallons of gas.  Who had better gas mileage?

Tom = 12.5

Ann = 15

400

Ronald can run 300 meters in 40 seconds.  It takes Carlos 30 seconds to run 200 meters. Who runs faster?

Ronald = 7.5

Carlos = 6.7

500

Three different stores sell packs of Pepsi.

Price Chopper sells 6-packs for $4.50.

Tops sells 12-packs for $8.50.

Walmart sells 30-packs for $18.

Who has the best buy?

Price Chopper = $0.75

Tops = $0.71

Walmart = $ 0.60

Prop. Relationships

100

A frozen yogurt stand opened this summer.  The cost is based on the weight. 

weight:   5          8          10

cost:       2.00     3.20     4.00

How much would 15 ounces cost?

$6.00

200

A recipe book provides the following cooking conversions.

cups:         1/2      1      1 1/2

ounces:      4         8      12

How many ounces are equal to 3 cups?

24 ounces

300

Alex spent the summer working to earn money to buy a gaming system.  After working for 4 weeks, he earned $112.  If the gaming system costs $250, does he have enough money after working for 9 weeks?

9 weeks = $252

yes

400

John is filling his bathtub.  It is 18 inches deep.  He notices that it takes 2 minutes to fill the tub with 3 inches of water.  How long will it take to fill the tub?

12 minutes

500

Mrs. Smith wants to make juice for her class.  The directions say to mix 2 scoops of powdered drink mix with a half gallon of water to make a pitcher of juice.  One of her students said that she will mix 8 scoops with 2 gallons to make 4 pitchers.  Is she correct?

Yes

Proportional?

100

Is y proportional to x? Why or why not?

x        y

3        12

5        10

2        8

No, the unit rate is not the same

200

Is y proportional to x? Why or why not?

x        y

6        4

12      8

3        2

Yes, the unit rate is constant.

300

It is snowing again. The amount of snowfall in inches is compared to the amount of time in hours it snows in five counties. Is y proportional to x? Why or why not?

time (x)      2     6     8     2.5     7

inches (y)   10   12   16    5       14

No, not a constant unit rate

400

The cost of a movie in dollars is compared to the number of days a movie is rented. Is y proportional to x? Why or why not?

number of days (x)   6    9     24    3

cost in dollars (y)      2    3     8     1

Yes, the unit rate is 1/3

500

Look at the graph that is drawn.  Does it show a proportional relationship.  Why or why not?

No, it is a straight line but does not start at (0,0)

Constant of Prop.

100

Tom drives 260 miles in 4 hours. 

What is the unit rate?

How far will he drive in 10 hours?

How long will it take him to drive 520 miles?

unit rate = 65

10 hours = 650 hours

520 miles = 8 hours

200

The dry cleaning fee is 3 pairs of pants for $18.

What is the unit rate?

How much for 11 pairs of pants?

How many pairs of pants can be cleaned for $102?

unit rate = 6

11 pairs of pants =$66

$102 = 17

300

Scientists wondered if the deer population is constant across the National Forest. One scientist counted 144 deer in 16 sq. miles.  Another counted 117 deer in 13 sq. miles.  A third scientist counted 216 deer in 24 sq. miles. 

Is the population of deer constant? How do you know?

How many sq. miles would you find 486 deer?

Yes, constant of proportionality is 9

486 deer = 54 sq. miles

400

Suzette and Margo want to make crepes for all their classmates. A recipe makes 20 crepes with a certain amount of water and flour and 2 eggs.  They have plenty of flour and milk to make 50 crepes.  They need to determine the number of eggs they will need.

How many eggs are needed to make 50 crepes?

How many crepes could they make with 11 eggs?

50 crepes = 5 eggs

11 eggs = 110 crepes

500

Brandon came home from school and told his mother he needed cookies for his entire grade level. He needs 3 cookies for each of the 96 students in the 7th grade.  His mother can fit 36 cookies on two cookie sheets.  If takes 2 hours to bake 8 sheets of cookies.  How long will it take to finish baking the cookies for the bake sale?

4 hours

y = kx

100

Write an equation in y = kx

Johnny drives his car 300 miles and uses 12 miles of gas.  Relate miles to gallons.

y = 25x

200

Write an equation in y = kx

Jordan earns $380 for working 40 hours.  Relate dollars to hours.

y = 9.5x

300

Susie can run 10 laps in 25 minutes.  Write an equation that shows the number of laps she can run per minute.

y = 0.4x

400

A person who weighs 100 pounds on Earth weighs 16.6 pounds on the moon.  Write an equation that relates the weight on Earth to weight on the moon.

y = 6.02x

500

In Kayla's car, the number of miles driven is proportional to the number of gallons uses.  Find the missing value.

gallons  0      4        6        ?        10

miles    0      112     168     224    280

Write an equation that relates the number of miles to gallons.

8 gallons

y = 28x