## Engage NY Eureka Math Grade 6 Module 4 Lesson 31 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 31 Example Answer Key

Example 1:

Marcus reads for 30 minutes each night. He wants to determine the total number of minutes he will read over the course of a month. He wrote the equation t = 30d to represent the total amount of time that he has spent reading, where t represents the total number of minutes read and d represents the number of days that he read during the month. Determine which variable is independent and which is dependent. Then, create a table to show how many minutes he has read in the first seven days.
Independent Variable: ________
Dependent Variable: _________

Independent Variable: Number of days

Example 2:

Kira designs websites. She can create three different websites each week. Kira wants to create an equation that will give her the total number of websites she can design given the number of weeks she works. Determine the independent and dependent variables. Create a table to show the number of websites she can design over the first 5 weeks. Finally, write an equation to represent the number of websites she can design when given any number of weeks.
Independent Variable: ________
Dependent Variable: _________
Equation: _______

Independent variable: # of weeks worked Worked (w)
Dependent variable: # of websites designed

Equation d = 3w, where w is the number of weeks worked and d is the number of websites designed.

Example 3:

Priya streams movies through a company that charges her a $5 monthly fee plus$1. 50 per movie. Determine the independent and dependent variables, write an equation to model the situation, and create a table to show the total cost per month given that she might stream between 4 and 10 movies in a month.
Independent Variable: ________
Dependent Variable: _________
Equation: _______

Independent variable: # of movies watched per month
Dependent variable: Total cost per month, in dollars
Equation: c = 1.5m + 5 or c = 1.50m + 5

### Eureka Math Grade 6 Module 4 Lesson 31 Exercise Answer Key

Exercises:

Exercise 1.
Sarah is purchasing pencils to share. Each package has 12 pencils. The equation n = 12p, where n is the total number of pencils and p is the number of packages, can be used to determine the total number of pencils Sarah purchased. Determine which variable is dependent and which is independent. Then, make a table showing the number of pencils purchased for 3 – 7 packages.

The number of packages, p, is the independent variable.
The total number of pencils, n, is the dependent variable.

Exercise 2.
Charlotte reads 4 books each week. Let b be the number of books she reads each week, and let w be the number of weeks that she reads. Determine which variable is dependent and which is independent. Then, write an equation to model the situation, and make a table that shows the number of books read in under 6 weeks.

The number of weeks, w, is the independent variable.
The number of books, b, is the dependent variable.
b = 4w

Exercise 3.
A miniature golf course has a special group rate. You can pay $20 plus$3 per person when you have a group of 5 or more friends. Let f be the number of friends and c be the total cost. Determine which variable is independent and which is dependent, and write an equation that models the situation. Then, make a table to show the cost for 5 to 12 friends.

The number of friends, f, is the independent variable.
The total cost in dollars, c, is the dependent variable.
c = 3f +20

Exercise 4.
Carlos is shopping for school supplies. He bought a pencil box for $3, and he also needs to buy notebooks. Each notebook is$2. Let t represent the total cost of the supplies and n be the number of notebooks Carlos buys. Determine which variable is independent and which is dependent, and write an equation that models the situation. Then, make a table to show the cost for 1 to 5 notebooks.

The total number of notebooks, n, is the independent variable.
The total cost in dollars, t, is the dependent variable.
t = 2n + 3

### Eureka Math Grade 6 Module 4 Lesson 31 Problem Set Answer Key

Question 1.
Jazlyah sells 3 houses each month. To determine the number of houses she can sell in any given number of months, she uses the equation t = 3m, where t is the total number of houses sold and m is the number of months. Name the independent and dependent variables. Then, create a table to show how many houses she sells in fewer than 6 months.

The independent variable is the number of months. The dependent variable is the total number of houses sold.

Question 2.
Joshua spends 25 minutes of each day reading. Let d be the number of days that he reads, and let m represent the total minutes of reading. Determine which variable is independent and which is dependent. Then, write an equation that models the situation. Make a table showing the number of minutes spent reading over 7 days.

The number of days, d, is the independent variable.
The total number of minutes of reading, m, is the dependent variable.
m = 25d

Question 3.
Each package of hot dog buns contains 8 buns. Let p be the number of packages of hot dog buns and b be the total number of buns. Determine which variable is independent and which is dependent. Then, write an equation that models the situation, and make a table showing the number of hot dog buns in 3 to 8 packages.

The number of packages, p, is the independent variable.
The total number of hot dog buns, b, is the dependent variable.
b = 8p

Question 4.
Emma was given 5 seashells. Each week she collected 3 more. Let w be the number of weeks Emma collects seashells and s be the number of seashells she has total. Which variable is independent, and which is dependent? Write an equation to model the relationship, and make a table to show how many seashells she has from week 4 to week 10.

The number of weeks, w, is the independent variable.
The total number of seashells, s, is the dependent variable.
s = 3w + 5

Question 5.
Emilia is shopping for fresh produce at a farmers market. She bought a watermelon for $5, and she also wants to buy peppers. Each pepper is$0. 75. Let t represent the total cost of the produce and n be the number of peppers bought. Determine which variable Is independent and which is dependent, and write an equation that models the situation. Then, make a table to show the cost for 1 to 5 peppers.

The number of peppers, n, is the independent variable.
The total cost in dollars, t, is the dependent variable.
t = 0.75n + 5

Question 6.
A taxicab service charges a flat fee of $7 plus an additional$1.25 per mile driven. Show the relationship between the total cost and the number of miles driven. Which variable is independent, and which is dependent? Write an equation to model the relationship, and make a table to show the cost of 4 to 10 miles.

The number of miles driven, m, is the independent variable.
The total cost in dollars, c, is the dependent variable.
c = 125m + 7

### Eureka Math Grade 6 Module 4 Lesson 31 Exit Ticket Answer Key

For each problem, determine the independent and dependent variables, write an equation to represent the situation, and then make a table with at least 5 values that models the situation.

Question 1.
Kyla spends 60 minutes of each day exercising. Let d be the number of days that Kyla exercises, and let m represent the total minutes of exercise in a given time frame. Show the relationship between the number of days that Kyla exercises and the total minutes that she exercises.
Independent variable: _______
Dependent variable: ________
Equation: _______

Tables may vary.
Independent variable: Number of Days
Dependent variable: Total Number of Minutes
Equation: m = 60d

Question 2.
A taxicab service charges a flat fee of $8 plus an additional$1.50 per mile. Show the relationship between the total cost and the number of miles driven.
Independent variable: _______
Dependent variable: ________
Equation: _______