This task has multiple parts which build upon one another. Students will reason about rates using real-world scenarios. Have students work in groups to complete each part.

Part 1
When the denominator of a rate is 1, the rate is called a unit rate. How might the unit rate for this problem be determined?
120 eggs from 20 chickens
Identify a strategy from the list created to determine the unit rate for the following problems:
1. $55 for 20 people
2. 250 miles in 4 hours
3. 60 feet in 4 minutes
4. 48 books for 16 students Which is the better deal: 3 cans of soda for $1.27 or 5 cans of soda for $1.79?

1 answer

To determine the unit rate, we need to find out how many of each item corresponds to one unit in the denominator. Here's how we can break it down for each problem:

Part 1: Identifying Strategies for Finding Unit Rates

  1. $55 for 20 people:

    • To find the cost per person, divide the total amount by the number of people: \[ \text{Unit Rate} = \frac{55}{20} = 2.75 \text{ dollars per person} \]
  2. 250 miles in 4 hours:

    • To find the distance per hour, divide the total miles by the number of hours: \[ \text{Unit Rate} = \frac{250}{4} = 62.5 \text{ miles per hour} \]
  3. 60 feet in 4 minutes:

    • To find the feet per minute, divide the total distance by the total time: \[ \text{Unit Rate} = \frac{60}{4} = 15 \text{ feet per minute} \]
  4. 48 books for 16 students:

    • To find the number of books per student, divide the total number of books by the number of students: \[ \text{Unit Rate} = \frac{48}{16} = 3 \text{ books per student} \]

Part 2: Comparing Costs of Cans of Soda

To compare the two deals — 3 cans of soda for $1.27 versus 5 cans of soda for $1.79 — we need to calculate the unit rate in terms of cost per can.

  1. 3 cans for $1.27: \[ \text{Cost per can} = \frac{1.27}{3} \approx 0.4233 \text{ dollars per can} \]

  2. 5 cans for $1.79: \[ \text{Cost per can} = \frac{1.79}{5} = 0.358 \text{ dollars per can} \]

Conclusion on Deals:

  • The unit rate for the first deal (3 cans for $1.27) is approximately $0.42 per can.
  • The unit rate for the second deal (5 cans for $1.79) is $0.36 per can.

Thus, the better deal is 5 cans of soda for $1.79, as it costs less per can.