Lesson 2.1
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes. Who runs faster?
Maura
Select all the rates that are unit rates:
A. 1 / 1/3
B. 2/3 / 1
C. 2/3
D. 3/1
E. 1/9
B. 2/3 / 1
D. 3/1
How do you know whether 2 quantities x and y are proportional?
Every ratio for y/x is equivalent
Write an equatoin that relates 2 proportional quantities x and y. Which variable represents the constant of proportionality?
y = kx
k represents the constant of proportionality
How do you know if an equation represents a proportional relationship?
An equation that can be written as y = kx
A group of 12 students is deciding whether to go to the science center or the zoo. Science center tickets are 3 for $36.75 and zoo tickets are 4 for $51.
How much will a group of 12 students save by choosing the science center?
$6
Yosef typed a 36-word paragraph in 2/3 minutes. What is his typing speed in words per minute?
54 words per minute
Is there a proportional relationship between x and y?
x: 8, 10, 12, 14
y: 5, 7, 9, 11
No
Which equation represents a proportional relationship?
A. y = 7x - 3
B. y = 150x
C. y = 21/x
D. y = 2x + 1
B. y = 150x
Ana runs 3/4 miles in 6 minutes. Assuming she runs at a constant rate, what is her speed in miles per hour?
7.5 miles per hour
Clara and Toby are telemarketers. Yesterday, Clara reached 4 people in 10 phone calls, while Toby reached 3 people in 8 phone calls. If each telemarketer continues at the same rate, who will reach more pople in 40 calls?
Clara
Kelly is knitting a scarf for her brother. It took her 1/3 hour to knit 3/8 foot of the scarf. How fast is Kelly's knitting speed in feet per hour.
1 1/8 feet per hour
Are the two quantities proportional?
x: 3, 90, 120
y: 2, 60, 80
Yes
Each ratio = 2/3
The equation y = 0.25x describes a proportional relationship between x and y. What is the constant of proportionality?
0.25
A trail mix recipe includes granola, oats, and almonds. There are 135 calories in a 1/4 cup serving of the trail mix. How many calories are in 2 cups of trail mix?
1,080 calories
Which of the following statements about unit rates is NOT true?
A. A unit rate relates a quantity to 1
B. Unit rates can be used to compare two rates
C. Any unit rate is equivalent to its unit rate
D. A unit rate always relates quantities with the same units
D. A unit rate always relates quantities with the same units
Stacy and Neil painted 280 feet of their living room wall with 4/5 gallons of paint. How many feet can they paint with 3 gallons of paint?
1,050 feet
The relationship between x and y is proportional. When x is 3, y is 51. What is x when y is 204?
12
The equation y = x/9 relates proportional quantities x and y. What is the value of x when y is 4?
36
Janet, Rosi, and Tanya buy postcards from their favorite souvenir shop. Janet buys 3 postcards for $1.05. Rosi buys 5 postcards for $1.75. Tanya buys 8 postcards for $2.80. Are the cost (y) in dollars and the number of postacrds (x) proportional? If so, write an equation to represent this equation.
Yes
y = 0.35x
Machine A pops 12.75 ounces of popcorn in 3 minutes. Machine B pops 18 ounces of popcorn in 4 minutes. If each machine pops popcorn for 10 minutes, will there be enough popcorn for eight 9-ounce bags?
Yes
Machine A + Machine B = 87.5 ounces
Harper knows he is 50 yards from school. The map on his phone shows that the school is 3/4 inch from his current location. If Harper's current location is 3 inches from home on the same map, how far is Harper from home?
200 yards
A recipe calls for 1 1/2 teaspoons of cinnamon to make 2 dozen oatmeal cookies. How many teaspoons of cinnamon are needed to make 60 oatmeal cookies?
3 3/4 teaspoons
The number of pizzas, y, and the weight of the shredded cheese topping, x, on the pizzas have a proportional relationship. When shredded, a 50-pound block of cheese is enough to make 150 large pizzas.
Find the constant of proportionality.
3
Four movie tickets cost $30. 5 concert tickets cost $36.50. Does the movie or the concert cost less per ticket? How much less?
The concert ticket costs $0.20 less per ticket than the movie.