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 This is a proportional

relationship. The unit rate is

18 cookies per sheet.

The constant of proportionality is 18.

8 144 144/8 = 18 cookies per sheet

4 72 72/4 = 18 cookies per sheet

2 36 36/2 = 18 cookies per sheet

1b. How many cookies does Brandon need to bake for the Bake Sale?

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?

96 students ( 3 cookies per student)=288 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.

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

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.

The unit rate is $4.50 per game.

The constant of proportionality is 4.50.

4 18 $18/4 = $4.50 per game

6 27 $27/6 = $4.50 per game

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