2.1 - CONNECT RATIOS, RATES, & UNIT RATES
Which of the following statements about unit rates is NOT true?
A. A unit rate relates a quantity to 1.
B. Unite rates can be used to compare two rates.
C. Any 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.
If there are 75 calories in half of a Twinkie bar, how many calories are in 6 Twinkie bars?
900 calories in 6 Twinkie bars
How do you know whether two quantities x and y are proportional?
A. Every ratio y/x for related pairs of x and y is equivalent.
B. Every sum x + y is the same for related pairs of x and y.
C. Every x term is a multiple of the previous term.
D. Every difference x- y is the same for related pairs of x and y.
A. Every ratio y/x for related pairs of x and y is equivalent.
Write an equation that relates two proportional quantities x and y.
Which variable represents the constant of proportionality?
y = kx; k represents the constant of proportionality.
Maura runs 5 miles in 1.25 hours. Ava runs 3 miles in 50 minutes, or 0.83 hour. Who runs faster?
Maura
Yosef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
54 words per minute
Is there a proportional relationship between x and y? Explain.
x 8 10 12 14
y 5 7 9 11
A. No; all ratios y/x are not equivalent.
B. Yes; each x value and y value increases by 2.
C. Yes; the difference between each x value and y value is 3.
D. No; all ratios x/y are greater than 1.
A. No; all ratios y/x are not equivalent.
Which equation represents a proportional relationship?
A. y = 7x - 3
B. y = 150x
C. y = 21/x
D. y = 2x + 1
B. y = 150x
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 people in 40 calls? How many more?
Clara; 1 person
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
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= 0.25x describes a proportional relationship between x and y. What is the constant of proportionality?
0.25
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
Stacy and Neil painted 280 ft2 of their living room wall with 4/5 gallon of paint. How many square feet can they paint with 3 gallons of paint?
1,050ft2
The table shows the numbers of snare drum backbeats and bass guitar notes in a disco song. Are the two quantities proportional? Explain.
Snare Drum Backbeats
3 90 120
Bass Guitar Notes
2 60 80
Yes; All the ratios of backbeats to notes are equivalent.
The equation y = 9x relates proportional quantities x and y.
What is the value of x when y is 4?
36
Machine A pops 12.75 ounces of popcorn in 3 minutes. Machine B pops 18 ounces od 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 and Machine B make 87.5 ounces in 10 minutes.
87.5 > 72, so there will be enough popcorn.
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
Shipping rates for Company A and Company B are shown in the tables below. Which company has shipping rates that represent a proportional relationship? Explain.
Company B; The ratios of cost to weight are equivalent.