Lesson 16Two Related Quantities (Part 1)
Learning Goal
Let’s use equations and graphs to describe relationships with ratios.
Learning Targets
I can create tables and graphs that show the relationship between two amounts in a given ratio.
I can write an equation with variables that shows the relationship between two amounts in a given ratio.
Lesson Terms
- dependent variable
- independent variable
Warm Up: Which One Would You Choose?
Problem 1
Which one would you choose? Be prepared to explain your reasoning.
A 5-pound jug of honey for $15.35
Three 1.5-pound jars of honey for $13.05
Activity 1: Painting the Set
Problem 1
Lin needs to mix a specific shade of orange paint for the set of the school play. The color uses 3 parts yellow for every 2 parts red.
Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs.
cups of red paint
cups of yellow paint
total cups of paint
Lin notices that the number of cups of red paint is always
of the total number of cups. She writes the equation to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know. Write an equation that describes the relationship between
and where is the independent variable. Write an equation that describes the relationship between
and where is the independent variable. Use the points in the table to create two graphs that show the relationship between
and . Match each relationship to one of the equations you wrote. 
Print Version
Lin needs to mix a specific shade of orange paint for the set of the school play. The color uses 3 parts yellow for every 2 parts red.
Complete the table to show different combinations of red and yellow paint that will make the shade of orange Lin needs.
cups of red paint
cups of yellow paint
total cups of paint
Lin notices that the number of cups of red paint is always
of the total number of cups. She writes the equation to describe the relationship. Which is the independent variable? Which is the dependent variable? Explain how you know. Write an equation that describes the relationship between
and where is the independent variable. Write an equation that describes the relationship between
and where is the independent variable. Use the points in the table to create two graphs that show the relationship between
and . Match each relationship to one of the equations you wrote.
Are you ready for more?
Problem 1
A fruit stand sells apples, peaches, and tomatoes. Today, they sold 4 apples for every 5 peaches. They sold 2 peaches for every 3 tomatoes. They sold 132 pieces of fruit in total. How many of each fruit did they sell?
Lesson Summary
Equations are very useful for describing sets of equivalent ratios. Here is an example.
A pie recipe calls for 3 green apples for every 5 red apples. We can create a table to show some equivalent ratios.
green apples (g) | red apples (r) |
|---|---|
We can see from the table that
When we know the number of green apples and want to find the number of red apples, we can write:
In this equation, if changes, is affected by the change, so we refer to as the independent variable and as the dependent variable. We can use this equation with any value of
to find . If 270 green apples are used, then or 450 red apples are used.
When we know the number of red apples and want to find the number of green apples, we can write:
In this equation, if changes, is affected by the change, so we refer to as the independent variable and as the dependent variable. We can use this equation with any value of
to find . If 275 red apples are used, then or 165 green apples are used.
We can also graph the two equations we wrote to get a visual picture of the relationship between the two quantities.
