The Constant
of Proportionality
(a.k.a: the unit rate)
Example 1: After school, Brandon told his
Mom that he had volunteered to make
cookies for the school’s Bake Sale. He planned
to make 3 cookies for each of the 96 students
in 7th grade. Brandon’s Mom told him that he
could bake 36 cookies on two cookie sheets.
1a. Is the number of cookies baked proportional to the number of cookie
sheets used? Complete the table below to organize the information.
# of
cookie
sheets
# of
cookies
baked
# of cookies baked
# of cookie sheets
2
36
36/2 = 18 cookies per sheet
4
72
72/4 = 18 cookies per sheet
8
144
144/8 = 18 cookies per sheet
This is a proportional
relationship.
The unit rate is
18 cookies per sheet.
The constant of
proportionality is 18.
1b. How many cookies does Brandon need to bake for the Bake
Sale?
96 students ( 3 cookies per student)
=288 cookies
1c. It took 2 hours to bake 8 sheets of cookies. If Brandon and his
Mom start baking at 4:00 p.m., when will they finish baking
cookies?
288 cookies .
18 cookies per sheet
=16 sheets of cookies needed
If it took 2 hours to bake 8 sheets of cookies, it will take 4 hours
to bake 16 sheets of cookies. They will finish baking at 8 p.m.
Example 2: Last week, Lenny spent $18 to bowl 4
games. This week, he spent $27 to bowl 6 games.
Lenny owns his own bowling ball and shoes, so he
only has to pay for each game that he bowls.
2a. If each of the games costs the same amount of money, what is the
constant of proportionality between the money spent and the number
of games played? Complete the table below to organize the information.
# of
games
Money
spent ($)
Money spent
# of games
4
18
$18/4 = $4.50 per game
6
27
$27/6 = $4.50 per game
The unit rate is $4.50 per game.
The constant of proportionality is 4.50.
2b. If Lenny bowls 9 games in the tournament next weekend, how
much will he have to pay?
Total amount spent = (cost per game) (number of games)
Total amount spent = (4.50) (9)
Total amount spent = $40.50