## Engage NY Eureka Math Grade 6 Module 4 Lesson 32 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 32 Opening Exercise Answer Key

Opening Exercise:

Xin is buying beverages for a party that comes in packs of 8. Let p be the number of packages Xin buys and t be the total number of beverages. The equation t = 8p can be used to calculate the total number of beverages when the number of packages is known. Determine the independent and dependent variables in this scenario. Then, make a table using whole number values of p less than 6.

Answer:

The total number of beverages is the dependent variable because the total number of beverages depends on the number of packages purchased. Therefore, the independent variable is the number of packages purchased.

### Eureka Math Grade 6 Module 4 Lesson 32 Example Answer Key

Example 1:

Make a graph for the table in the Opening Exercise.

Answer:

→ To make a graph, we must determine which variable is measured along the horizontal axis and which variable is measured along the vertical axis.

→ Generally, the independent variable is measured along the x-axis. Which axis is the x-axis?

The x-axis is the horizontal axis.

→ Where would you put the dependent variable?

On the y-axis. It travels vertically, or up and down.

→ We want to show how the number of beverages changes when the number of packages changes. To check that you have set up your graph correctly, try making a sentence out of the labels on the axes. Write your sentence using the label from the y-axis first followed by the label from the x-axis. The total number of beverages depends on the number of packages purchased.

Example 2:

Use the graph to determine which variable is the independent variable and which is the dependent variable. Then, state the relationship between the quantities represented by the variables.

Answer:

The number of miles driven depends on how many hours they drive. Therefore, the number of miles driven is the dependent variable, and the number of hours is the independent variable. This graph shows that they can travel 50 miles every hour. So, the total number of miles driven increases by 50 every time the number of hours increases by 1.

### Eureka Math Grade 6 Module 4 Lesson 32 Exercise Answer Key

Exercises:

Exercise 1.

Each week Quentin earns $30. If he saves this money, create a graph that shows the total amount of money Quentin has saved from week 1 through week 8. Write an equation that represents the relationship between the number of weeks that Quentin has saved his money, w, and the total amount of money in dollars that he has saved, s. Then, name the independent and dependent variables. Write a sentence that shows this relationship.

Answer:

s = 30w

The amount of money sowed in dollars, s, is the dependent variable, and the number of weeks, w, is the independent variable.

Therefore, the amount of money Quentin has saved increases by $30 for every week he saves money.

Exercise 2.

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

Answer:

The number of weeks is the independent variable. The number of books collected is the dependent variable.

Exercise 3.

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

Answer:

t = 3r + 5

The number of rides is the independent variable, and the total cost in dollars, is the dependent variable.

### Eureka Math Grade 6 Module 4 Lesson 32 Problem Set Answer Key

Question 1.

Caleb started saving money in a cookie jar. He started with $25. He adds $10 to the cookie jar each week. Write an equation where w is the number of weeks Caleb saves his money and t is the total amount in dollars in the cookie jar. Determine which variable is the independent variable and which is the dependent variable. Then, graph the total amount in the cookie jar for w being less than 6 weeks.

Answer:

t = 10w + 25

The total amount, t, is the dependent variable.

The number of weeks, w, is the independent variable.

Question 2.

Kevin is taking a taxi from the airport to his home. There is a $6 flat fee for riding In the taxi. In addition, Kevin must also pay $1 per mile. Write an equation where m is the number of miles and t is the total cost in dollars of the taxi ride. Determine which variable is independent and which is dependent. Then, graph the total cost for m being less than 6 miles.

Answer:

t = 1m + 6

The total cost in dollars, t, is the dependent variable.

The number of miles, m, is the Independent variable.

Question 3.

Anna started with $10. She saved an additional $5 each week. Write an equation that can be used to determine the total amount saved in dollars, t, after a given number of weeks, w. Determine which variable Is independent and which is dependent. Then, graph the total amount saved for the first 8 weeks.

Answer:

t = 5w + 10

The total amount saved in dollars, t, is the dependent variable.

The number of weeks, w, is the independent variable.

Question 4.

Aliyah is purchasing produce at the farmers’ market. She plans to buy $10 worth of potatoes and some apples. The apples cost $1. 50 per pound. Write an equation to show the total cost of the produce, where T is the total cost, in dollars, and a is the number of pounds of apples. Determine which variable is dependent and which is independent. Then, graph the equation on the coordinate plane.

Answer:

T = 1.50a + 10

The total cost in dollars is the dependent variable. The number of pounds of apples is the independent variable.

### Eureka Math Grade 6 Module 4 Lesson 32 Exit Ticket Answer Key

Question 1.

Determine which variable is the independent variable and which variable is the dependent variable. Write an equation, make a table, and plot the points from the table on the graph. Enoch can type 40 words per minute. Let w be the number of words typed and m be the number of minutes spent typing.

Answer:

The independent variable is the number of minutes spent typing. The dependent variable is the number of words typed. The equation is w = 40m.