Unit Rate and C o P
Name ________________ P __
Track labels while calculating your constant of proportionality!
Constants of Proportionality are really unit rates.
The denominator label represents the quantity you divided by (divisor). This is the “unit” in your unit rate!
PART 1: A new car can hold 11.2 gallons of gas in a tank, and travels 448 miles before refueling.
1) Find both unit rates present in this gallons to miles relationship.
a. Find the Constant of Proportionality k so that k(gallons) = miles.
b. Find the Constant of Proportionality c so that c(miles) = gallons.
2) By remembering the units in our work, we can see each Constant of Proportionality as a unit rate.
a. Which unit rate does k represent?
k is _________ per __________
b. Which unit rate does c represent?
c is _________ per __________
PART 2: At the store, 16 apples cost $3.20.
3) Write a constant of proportionality equation that would find the cost of a single apple. Then solve to find the
unit rate per apple.
4) Write a constant of proportionality equation that would find the number of apples you can buy for a dollar.
Then solve to find the unit rate per dollar.
PART 3: The ratio table below shows a variety of candy bar purchases at the same store.
Price
Candy Bars
$3.20
8
$4.40
11
$9.20
23
$1.20
3
$10.40
26
$2.00
5
5) John wants to find the cost per candy bar.
Here is his work:
k=
k=
(𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠)
(𝑑𝑜𝑙𝑙𝑎𝑟𝑠)
8 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠
$3.20
Explain to John why his strategy will not give the unit rate he is hoping for. Why not?
6) Amanda wants to find the cost per candy bar.
Here is her work:
k(𝑑𝑜𝑙𝑙𝑎𝑟𝑠) = (candy bars)
k($3.20) = 8 candy bars
k=
8 𝑐𝑎𝑛𝑑𝑦 𝑏𝑎𝑟𝑠
$3.20
Amanda has the same problem as John! Rewrite her original equation so it will produce the unit rate she wants
to find. What should be different?
7) What is the price per candy bar? Write a Constant of Proportionality equation and solve!
8) How many candy bars can you buy for a dollar? Write a Constant of Proportionality equation and solve!