Unit Rates and Ratios
A baker uses 8 cups of flour to make 48 cookies. What is the unit rate of cookies per cup of flour?
6 cookies per cup of flour
How can you tell if a relationship shown on a graph is proportional?
The graph must be a straight line that passes through the origin (0,0)
A graph of money earned (y) vs. hours worked (x) contains the point (1, 18.50). What does this point represent?
The pay rate is $18.50 per hour.
If a scale drawing uses a scale factor of 5, what do you do to the original lengths to get the new lengths?
Multiply the original lengths by 5.
A square has a side length of 6 cm. What is its area?
36
A runner completes 3/4 of a mile in 1/10 of an hour. What is the runner's speed in miles per hour?
7.5 or 7 1/2
Is the equation y = 7x - 2 proportional? Why or why not?
No, because when x = 0, y = -2 (it does not pass through the origin).
If a car travels at a constant speed of 65 miles per hour, write an equation for total distance $d$ in terms of hours $h$.
d = 65h
A rectangular garden is 12 feet long and 8 feet wide. A scale drawing is made using a scale factor of 1/4. What are the dimensions of the drawing?
3 feet by 2 feet
If all side lengths of a polygon are multiplied by a scale factor of 3, by what factor does the area change?
9
Brand A sells a 16-ounce jar of honey for $4.80. Brand B sells a 20-ounce jar for $5.60. Which brand is the better buy per ounce?
Brand B.
A table lists the pairs (2, 7), (4, 14), and (6, 21). Is y proportional to x? Explain.
Yes, because the ratio 3.5 is constant for every pair.
A line on a graph passes through the origin and the point (4, 18). What is the constant of proportionality (k)?
k=4.5
On a map, 2 centimeters represents 50 miles in real life. How many miles are represented by 7 centimeters?
175 miles
A floor mat has an area of 10 sq ft. A similar mat is created using a scale factor of 2.5. What is the area of the larger mat?
62.5
A juice recipe calls for 2/5 cup of concentrate for every 1/2 cup of water. How many cups of concentrate are needed per 1 cup of water?
4/5 cups of concentrate
A taxi company charges a flat fee of $3.00 plus $2.00 per mile driven. Is the total cost proportional to the number of miles?
No, the flat fee makes the cost non-proportional because 0 miles would still cost $3.00.
A water pump fills a tank at a constant rate, given by the equation g = 8.5t, where g is in gallons and t is in minutes. How long does it take to pump 102 gallons?
12 minutes
A photo is shrunk down using a scale factor of 2/3. What scale factor would resize the mini photo back to its original size?
3/2
An original poster has an area of 100 sq in. A shrunk copy of the poster has an area of 25 sq in. What scale factor was applied to the side lengths?
1/2
Machine X produces 135 parts in 3 hours. Machine Y produces 220 parts in 5 hours. How many more parts per hour does Machine Y make than Machine X?
1 more part per hour.
Does the equation y = 0.85x represent a proportional relationship? What is the constant of proportionality?
Yes, 0.85
The point (1, k) lies on the graph of a proportional relationship. What does the y-value k represent?
k represents the unit rate (or constant of proportionality).
Model A is created with a scale factor of 1/2 from an original object. Model B is created with a scale factor of 5/2 from Model A. What scale factor transforms the original model directly into Model B?
5/4
Student A says "If I double the side lengths of a rectangle, the area doubles." Student B says "No, the area quadruples." Who is correct and why?
Student B is correct.