Unit Rates and Unit Price
Unit Rates with Fractions
Proportional Relationships
Constant of Proportionality
Graphing Proportions
100
An airplane on autopilot took 5 hours to travel 3,475 kilometers. What is the unit rate for kilometers per hour?
The unit rate is 695 kilometers per hour.
100
Yousef typed a 36-word paragraph in 2/3 minute. What is his typing speed, in words per minute?
54 words per minute
100
Does the table below show a proportional relationship? SHOW YOUR WORK TO SHOW HOW YOU KNOW.
YES the table shows a proportional relationship because relationship of every y to every x has a unit rate of 20.
100
A recipe calls for 3 ounces of flour for every 2 ounces of sugar. Find the constant of proportionality.
The constant of proportionality is 1.5
100
Which of the following graphs shows a proportional relationship?
A.) B.) C.)
Graph A shows a proportional relationship
200
What is the unit rate in meters per second if a car travels 374 meters in 17 seconds?
The unit rate is 22 meters per second.
200
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
200
Does the table below show a proportional relationship? SHOW YOUR WORK TO SHOW HOW YOU KNOW.
YES the table shows a proportional relationship because relationship of every y to every x has a unit rate of 3.5.
200
You bike 11.2 miles in 1.4 hours at a steady rate. Find the Constant of Proportionality. What equation represents the proportional relationship between the x hours you bike and the distance y in miles that you travel?
The Constant of Proportionality is 8. The equation y=8x represents the distance y in miles you bike in x hours.
200
The graph shows a proportional relationship between the number of miles and the number of hours Marco bikes. What equation relates the distance, y, and the time, x?
y = 15x
300
A store sells a package of 25 trading cards for $5.25. Find the unit price for the package of cards.
The unit price is $0.21 per card
300
A recipe calls for 1/2 cup of ingredient A for every
1 2/3 cups of ingredient B. You use 4 cups of ingredient A. How many cups of ingredient B do you need?
You need 13 1/3 cups of ingredient B
300
Complete the table then decide whether the table shows a proportional relationship between x and y. SHOW YOUR WORK TO EXPLAIN HOW YOU KNOW.
The table DOES NOT show a proportional relationship because the relationship between the x and y values does not show the SAME unit rate.
300
What is the constant of proportionality for the relationship between the number of milliliters y of water in the bowl and the time in seconds x? What is the equation?
The constant of proportionality is 16
The equation is y=16x.
300
Melanie buys 2 shells for $0.80. Rosi buys 3 shells for $1.20. Carlos buys 4 shells for $1.60. Use the graph to determine whether there is a proportional relationship between the number of shells and their cost. If so, what is the constant of proportionality in this situation?
The relationship between the number of shells and their cost is proportional.
The constant of proportionality in this situation is 0.40.
400
In one game, the ratio of three-point baskets to three-point tries for one team was 3:4. If the team scored 27 points from three-point baskets, how many three-point tries did the team have?
The team had 12 three-point tries.
400
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?
1050 ft2
400
Decide whether the table shows a proportional relationship between x and y. SHOW YOUR WORK TO EXPLAIN HOW YOU KNOW.
The table DOES NOT show a proportional relationship between x and y
400
The width of a row of identical townhouses is in a proportional relationship with the number of townhouses. The diagram suggests a row of 5 townhouses and gives their total width.
a.) Find the constant of proportionality.
b.) Write the equation for the relationship.
c.) Use the constant of proportionality to find the width of a row of 9 townhouses.
a.) The constant of proportionality is 21 feet per townhouse.
b.) The equation is y=21x
c.) The width of 9 townhouses is 189 feet.
400
The graph shows a proportional relationship between time and number of boxes a machine packages.
a.) What equation relates the number of boxes, y, and the time, x?
b.) How many boxes does the machine package in 9 minutes?
a.) y = 20x
b.) The machine packages 180 boxes in 9 minutes.
500
At a supermarket, a 6-ounce bottle of brand A salad dressing costs $1.56. A 14-ounce bottle costs $3.36. A 20-ounce bottle costs $5.60. What is the best buy?
The 14 ounce bottle is the best buy
500
A store sells two kinds of candles, scented and unscented. The scented candles burn 1/8 inch in 1/4 hour. The unscented candles burn 1/9 inch in 1/3 hour.
a.) What is the unit rate for inches burned per hour for EACH kind of candle?
b.) Which kind of candle burns more in an hour?
a.) The unit rate for the scented candles is 1/2
inch per hour.
The unit rate for the unscented candles is 1/3 inch per hour.
b.) The SCENTED candles burn more in an hour.
500
a.) Looking at the table, is the relationship between number of towers and number of customers proportional? SHOW YOUR WORK TO EXPLAIN HOW YOU KNOW.
b.) If there are 560 towers, how many customers does the company have? SHOW YOUR WORK.
a.) YES the relationship between number of towers and number of customers is proportional.
b.) The company would have 10,000 customers if there were 560 towers
500
For every 3 lemons you buy at a farm stand, the total cost increases by $1.80.
a.) Find the Constant of Proportionality
b.) Write an equation that relates the total cost y and the number of lemons x.
c.) Complete the Table below using the Constant of Proportionality.
a.) The constant of proportionality is 0.6
b.) An equation that relates the total cost y and the number of lemons x is y=0.6x
c.) 
500
A foreign country uses the stellar as its currency. Before a trip to that country, Jon wants to exchange $1,400 to stellars.
a.) Which of Bank A and Bank B has the better exchange rate?
b.) How many MORE stellars would he get if he exchanged his $1,400 at the better exchange rate instead of at the other rate?
a.) Bank B has the better exchange rate
b.) Jon would get 140 more stellars if he exchanged his $1,400 at Bank B