Better Buy
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
A frozen yogurt stand opened this summer. The cost is based on the weight in ounces.
weight: 5 8 10
cost: 2.00 3.20 4.00
How much would 15 ounces cost?
$6.00
Is y proportional to x? Why or why not?
x y
3 12
5 10
2 8
No, the unit rate is not constant
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 mph
10 hours = 650 miles
520 miles = 8 hours
Write an equation in y = kx
Johnny drives his car 300 miles and uses 12 miles of gas. Relate miles to gallons.
y = 25x
Weis 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?
*Weis = $1.67
Walmart = $1.70
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
Is y proportional to x? Why or why not?
x y
6 4
12 8
3 2
Yes, the rate is constant.
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 per pair
11 pairs of pants =$66
$102 = 17 pairs of pants
Write an equation in y = kx
Jordan earns $380 for working 40 hours. Relate dollars to hours.
y = 9.5x
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 mpg
Ann = 15 mpg
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
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
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
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
Ronald can run 300 meters in 40 seconds. It takes Carlos 30 seconds to run 200 meters. Who runs faster?
*Ronald = 7.5 meters per sec
Carlos = 6.7 meters per sec
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
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 rate is $1/3 per day
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
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. Round k to the nearest hundredth.
y = 6.02x
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
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
Look at the graph on your paper. Does it show a proportional relationship. Why or why not?
No, it is a straight line but does not start at (0,0)
David is making his own strawberry yogurt. In David’s mixture, the number of strawberries is proportional to the amount of milk, in cups. David uses 4 cups of milk for every 14 strawberries in his mixture. Write an equation that represents the relationship between y, the number of strawberries, and x, the number of cups of milk he uses?
y = 3.5 x
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