This document describes a math lesson on multi-step word problems involving equations. It includes examples of setting up equations to represent relationships between variables in real-world scenarios involving buying beverages, saving money each week, collecting books, and the cost of rides at a fair. Students are asked to identify independent and dependent variables, create tables and graphs modeling the equations, and write sentences describing the variable relationships. The closing asks students to check a friend's work on a taxi cab cost problem, where the friend has identified the variables incorrectly.

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Problem Set Lesson 31 answers

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MODULE 4 Expressions and Equaons
Topic H: Applicaons of Equaons
Lesson 32: Mul‐Step Problems in the Real World
Student Outcomes
§ Students analyze an equaon in two variables, choose an independent variable and a
dependent variable, make a table and make a graph for the equaon by plong the
points in the table. For the graph, the independent variable is usually represented by the
horizontal axis and the dependent variable is usually represented by the vercal axis.

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Classwork Opening Exercise
Xin is buying beverages for a party, which are individually packaged and come in
packs of 8. Let p be the number of packages Xin buys and t be the total number
of beverages. The equaon t = 8p can be used to calculate the total number of
beverages when the number of packages is known. Determine the independent
and dependent variable in this scenario. Then make a table using whole number
values of p less than 6.

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Example 1
Make a graph for the table in the Opening Exercise.

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Example 2
Use the graph to determine which variable is the independent variable and which is
the dependent variable. Then state the relaonship between the quanes
represented by the variables.
independent variable:
dependent variable:
relaonship between the quanes :

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Exercises
1. Each week Quenn earns $30. If he saves this money, create a graph
that shows the total amount of money Quenn has saved from week 1
through week 8. Write an equaon that represents the relaonship
between the number of weeks that Quenn has saved his money (w) and
the total amount of money he has saved (s). Then name the independent
and dependent variable. Write a sentence that shows this relaonship.

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2. Zoe is collecng books to donate. She started with 3 and collects two more each
week. She is using the equaon b = 2w + 3 , where b is the total number of books
collected and w is the number of weeks she has been collecng. Name the
independent and dependent variables. Then create a graph to represent how many
books Zoe has collected when w is 5 or less.

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3. Eliana plans to visit the fair. She must pay $5 to enter the fair grounds and an
addional $3 per ride. Write an equaon to show the relaonship between r, the
number of rides, and t, the total cost. State which variable is dependent and which is
independent. Then create a graph that models the equaon.

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Closing
Please take out your exit ticket for Lesson 32, close your
binder, and complete the exit ticket. This will be collected.
§Imagine that you are helping a friend with his math work. Here is the problem he was
solving:
Henry is taking a taxi cab home. The cab company charges an inial fee of $5 plus $2 for
each addional mile. Henry uses the equaon t = 2m + 5 to calculate the cost of the ride,
where t is the total cost and m is the number of miles.
Your friend states that t is the dependent variable and
m is the independent variable.
Then the friend starts to sketch a graph.
§What would you tell your friend when looking over his/her work?