Ratios and rates (ratio tables, unit rate) Knowledge-Based Practice

Questions

1. 1.

   A ratio table shows that an automated packaging machine fills 42 identical cartons in 3.5 minutes at a constant rate. What is the unit rate in seconds per carton?

   • A) 5 seconds per carton
   • B) 12 seconds per carton
   • C) 0.2 seconds per carton
   • D) 15 seconds per carton
2. 2.

   In a ratio table representing a proportional relationship, the pair (5, 17.5) represents the values of $x$ and $y$, respectively. If the value of $x$ increases from 8 to 14, by how much does the value of $y$ increase?

   • A) 21
   • B) 49
   • C) 28
   • D) 35
3. 3.

   A ratio table shows that 9 cups of flour are mixed with 6 cups of sugar in a recipe. If the recipe is scaled up to use 15 cups of sugar, how many more cups of flour than sugar are in the new mixture?

   • A) 7.5 cups
   • B) 9.0 cups
   • C) 13.5 cups
   • D) 22.5 cups
4. 4.

   Pump A fills 72 gallons of water in 6 minutes, and Pump B fills 91 gallons of water in 7 minutes, both operating at constant rates. If both pumps operate together at these rates, how many gallons of water will they fill in 15 minutes?

   • A) 180 gallons
   • B) 195 gallons
   • C) 375 gallons
   • D) 390 gallons
5. 5.

   A ratio table shows that a wind turbine generates 14 kilowatt-hours (kWh) of electricity in 35 revolutions at a constant rate. How many kilowatt-hours of electricity does the turbine generate in 80 revolutions?

   • A) 24 kWh
   • B) 32 kWh
   • C) 48 kWh
   • D) 200 kWh
6. 6.

   In a ratio table representing a proportional relationship between $x$ and $y$, every increase of 4 units in $x$ corresponds to an increase of 14 units in $y$. What is the value of $y$ when $x = 18$?

   • A) 63
   • B) 56
   • C) 70
   • D) 49
7. 7.

   In a ratio table representing a proportional relationship between $x$ and $y$, the unit rate is $\frac{3}{4}$ of a unit of $y$ for each unit of $x$. If $y = 36$, what is the value of $x$?

   • A) 27
   • B) 33
   • C) 45
   • D) 48
8. 8.

   A ratio table displays a proportional relationship between $x$ and $y$ where $y = 15$ when $x = 6$. If the table also contains the entries $(10, a)$ and $(b, 45)$, what is the value of $a + b$?

   • A) 22
   • B) 37
   • C) 55
   • D) 43
9. 9.

   A ratio table shows that an industrial printer produces 35 color brochures in 14 minutes at a constant rate. What is the unit rate in brochures per minute?

   • A) 0.4 brochures per minute
   • B) 2.1 brochures per minute
   • C) 2.5 brochures per minute
   • D) 2.8 brochures per minute
10. 10.

    A ratio table shows that an electric bus travels 54 miles in 1.5 hours and 126 miles in 3.5 hours at a constant speed. Which equation represents the relationship between the distance traveled in miles, $y$, and the time in hours, $x$?

    • A) $y = \frac{1}{36}x$
    • B) $y = 36x$
    • C) $y = x + 52.5$
    • D) $y = 54x$
11. 11.

    A ratio table shows that 18 yards of fabric cost $27 at a constant rate. What is the unit rate in yards of fabric per dollar?

    • A) $\frac{3}{2}$ yards per dollar
    • B) $\frac{2}{3}$ yard per dollar
    • C) $\frac{1}{3}$ yard per dollar
    • D) $\frac{3}{4}$ yard per dollar
12. 12.

    A water filtration system purifies 84 gallons of water in 3.5 hours at a constant rate. What is the unit rate of the system in gallons per hour?

    • A) 21 gallons per hour
    • B) 24 gallons per hour
    • C) 28 gallons per hour
    • D) 29.4 gallons per hour
13. 13.

    A ratio table shows that a commuter train travels 14 miles in 15 minutes and 42 miles in 45 minutes at a constant speed. What is the unit rate of the train in miles per hour?

    • A) 42 miles per hour
    • B) 56 miles per hour
    • C) 70 miles per hour
    • D) 84 miles per hour
14. 14.

    In a ratio table showing a proportional relationship, $y = 18$ when $x = 4$. Which pair of values $(x, y)$ belongs in the same table?

    • A) (6, 20)
    • B) (10, 45)
    • C) (8, 32)
    • D) (12, 36)
15. 15.

    An automated irrigation system waters $\frac{5}{6}$ of an acre of cropland in $\frac{2}{3}$ of an hour at a constant rate. What is the unit rate of the irrigation system in acres per hour?

    • A) $1\frac{1}{4}$ acres per hour
    • B) $\frac{5}{9}$ acre per hour
    • C) $\frac{4}{5}$ acre per hour
    • D) $1\frac{1}{2}$ acres per hour
16. 16.

    A ratio table relates the area of flooring installed to the time spent working at a constant rate. If 120 square feet are installed in 5 hours and 216 square feet in 9 hours, how many hours will it take to install 336 square feet?

    • A) 14 hours
    • B) 13 hours
    • C) 16 hours
    • D) 18 hours
17. 17.

    In a ratio table representing a constant packaging rate, 6 workers assemble a total of 45 gift boxes per hour. What is the unit rate of gift boxes assembled per worker each hour?

    • A) 6.5 gift boxes
    • B) 7.5 gift boxes
    • C) 8.0 gift boxes
    • D) 8.5 gift boxes
18. 18.

    In a drink recipe, the unit rate of water to concentrate is 2.5 cups of water per cup of concentrate. If a batch uses a total of 28 cups of liquid containing only water and concentrate in this ratio, how many cups of concentrate are used?

    • A) 7 cups
    • B) 8 cups
    • C) 11.2 cups
    • D) 20 cups
19. 19.

    Store A sells a 6-pack of identical notebooks for $15, while Store B sells an 8-pack of the same notebooks for$18. How much less does one notebook cost at Store B than at Store A?

    • A) $0.25
    • B) $0.50
    • C) $0.75
    • D) $1.25

Answers and step-by-step solutions appear after you finish the test.