Warm -up

At a local college, the ratio of girls to boys is 3:5. If there are 2700 girls, how many boys are there?

4500

xxxxx 6x=(5)8.40 X = 7 liters

PROPORTIONAL VS. NON-PROPORTIONALMonday, April 17, 2023

PROPORTIONAL VS. NON-PROPORTIONAL

If two quantities are proportional, then they have a constant ratio.

If the ratio is not constant, the two quantities are said to be non-proportional.

We will make tables and look at the relationship between the variables to determine proportionality.

PROPORTIONAL RELATIONSHIPS

Will always go through the origin on a graph. (0,0)

Graph will always be a straight line. Always write the constant ratio in the

form of

Reduce or divide to find the constant ratio for each.

y

x

PROPORTIONAL OR NON-PROPORTIONAL? In order to tell from a table if there is a

proportional relationship or not, you can check to see if the ratio is the same.

The ratio is also known as the scale factor.

y

x

y

x

EX 1. and 2.) Tell if the following tables represent a proportional relationships.

y

xx y

5 10

8 16

10 20

14 28

21 42

y

xx y

0 2

3 8

5 12

9 20

10 22

Proportional? ______ Ratio _________

Equation____________

Ordered Pair _________

Proportional?Ratio

Ordered Pair

In order to tell if a graph is proportional the line must go through the origin.

EX 3. and 4.) Tell if the following graphs represent a proportional relationships.

1 2 3 4 5

1

2

3

4

5

x

y

1 2 3 4 5

1

2

3

4

5

x

y

Proportional ? _________ Proportional ? _________

Why? Line goes thru the origin

Why? Line does notgo thru the origin

In order to tell if a set of ordered pairs is proportional, look at the ratio of y to x.

EX 5.) Tell if the following set of ordered pairs represents a proportional relationship.

8, 4 , 10, 5 , 5, 2.5 , 12, 6

Proportional? ______

Ratio _________

Equation ___________

Ordered Pair _________

EX 6. and 7.) Determine if the following equations show a proportional relationship.

Put a zero in for x; if y is zero then it is a proportional relationship because it goes through the origin.

y = 3x – 1 y = 10x

8. At HPMS, there are 26 students per teacher in advisory. Is the total number of students proportional to the number of teachers?

Teachers

1

Students 26

9. The City Pool costs $8 per day to visit during the summer. There is also a $25 yearly registration fee. Is the total cost proportional to the total number of days visited?

Day 1

Cost 33

EQUATIONS:

We will also make equations to describe each situation.

If the situation is proportional, you will use your constant ratio in your equation.

Make sure you define your variables!!!

EXAMPLE 1 IDENTIFY PROPORTIONAL RELATIONSHIPS

Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per order.

Write an equation to fit this situation:

11 2

x numberof pizzas sold

y Total Cost

x y

EXAMPLE 1 Sal’s Pizzeria sells large pizzas for $11 but charges a $2 delivery fee per order.

Write an equation that fits this situation: Hint: Use your constant ratio!!

4

x cupsof lemon juice

y cupsof water

x y

Ex. 2) A lemonade recipe calls for 1.5 cups of lemon juice and 6 cups of cold water.

Lemon Juice

Cups of Water

1.5 6

3 12

4.5 18

6 24

EXAMPLE 2 A lemonade recipe calls for 1.5 cups of lemon juice and 6 cups of cold water.

Ashley and Megan are running around a track. They run equally fast, but Ashley started later. When Ashley has run 5 laps, Megan has run 15 laps. When Ashley has run 30 laps, how many has Megan run?

Aunt Jo put 3 towels on the clothesline and Sue put 6. All of the towels are identical in terms of size, thickness, etc. It took 12 hours for Aunt Jo’s towels to dry. How long did it take Sue’s?

Proportional or Non-proportional?

The market has bags of apples on sale! Each bag contains the same number of apples. Your mom buys 2 bags and gets a total of 16 apples. Your grandmother buys 10 bags. How many apples did she get?

John owns a bakery. His recipe calls for 10 ounces of flour to make a pound of bread. How much bread will he make if he uses 23 ounces of flour?

The locomotive of a train is 12 meters long. If there are 4 carriages connected to the locomotive, the train is 52 meters long. If there were 8 carriages connected to the locomotive, how long would the train be?

Today, Molly becomes two years old and Daniel turns 6. When Molly is 12, how old will Daniel be?

•A group of 5 musicians plays a piece of music in 10 minutes. Another group of 35 musicians will play the same piece. How long will it take this group to play?

•Yesterday, a boat carrying 326 Toyota Corollas arrived in port. The total weight of the cars was 521 tons. Tomorrow, another boat will arrive into port carrying 732 Corollas. What will be the total weight of the cars?

•In the hallway at school, two rectangular tables are put together with short sides together. 10 chairs fit around the tables. A teacher wants to add four more tables, again putting short sides together. How many chairs will fit around the tables then?

HOMEWORK

Complete the Class Activity with a work buddy

Worksheet 4.3 “Proportional & Non-Proportional”