## Engage NY Eureka Math 6th Grade Module 4 Lesson 21 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 21 Example Answer Key

Look at Example 1 with your group. Determine the cost for various numbers of pizzas, and also determine the expression that describes the cost of having P pizzas delivered.

a. Pizza Queen has a special offer on lunch pizzas: $4.00 each. They charge $2.00 to deliver, regardless of how many pizzas are ordered. Determine the cost for various numbers of pizzas, and also determine the expression that describes the cost of having P pizzas delivered.

Number of Pizzas Delivered | Total cost in Dollars |

1 | |

2 | |

3 | |

4 | |

10 | |

50 | |

P |

Answer:

Number of Pizzas Delivered | Total cost in Dollars |

1 | 6 |

2 | 10 |

3 | 14 |

4 | 18 |

10 | 42 |

50 | 202 |

P | 4p + 2 |

What mathematical operations did you need to perform to find the total cost?

Answer:

Multiplication and addition. We multiplied the number of pizzas by $4 and then added the $2 delivery fee.

Suppose our principal wanted to buy a pizza for everyone in our class. Determine how much this would cost.

Answer:

Answers will vary depending on the number of students in your class.

b. If the booster club had $400 to spend on pizza, what is the greatest number of pizzas they could order?

Answer:

The greatest number of pizzas they could order would be 99. The pizzas themselves would cost 99 × $4 = $396, and then add $2.00 for delivery. The total bill is $398.

c. If the pizza price was raised to $5. 00 and the delivery price was raised to $3. 00, create a table that shows the total cost (pizza plus delivery) of 1, 2, 3, 4, and 5 pIzzas. Include the expression that describes the new cost of ordering P pizzas.

Number of Pizzas Delivered | Total Cost in Dollars |

1 | |

2 | |

3 | |

4 | |

5 | |

P |

Answer:

Number of Pizzas Delivered | Total Cost in Dollars |

1 | 8 |

2 | 13 |

3 | 18 |

4 | 23 |

5 | 28 |

P | 5p + 3 |

### Eureka Math Grade 6 Module 4 Lesson 21 Mathematical Modeling Exercise Answer Key

Mathematical Modeling Exercise

The Italian Villa Restaurant has square tables that the servers can push together to accommodate the customers. Only one chair fits along the side of the square table. Make a model of each situation to determine how many seats will fit around various rectangular tables.

Number of Square Tables | Number of seats at the Table |

1 | |

2 | |

3 | |

4 | |

5 | |

50 | |

200 | |

T |

Answer:

Number of Square Tables | Number of seats at the Table |

1 | 4 |

2 | 6 |

3 | 8 |

4 | 10 |

5 | 12 |

50 | 102 |

200 | 402 |

T | 2T + 2 or 2(T + 1) |

Are there any other ways to think about solutions to this problem?

Answer:

Regardless of the number of tables, there is one chair on each end, and each table has two chairs opposite one another.

It is impractical to make a model of pushing 50 tables together to make a long rectangle. If we did have a rectangle that long, how many chairs would fit on the long sides of the table?

Answer:

50 on each side, for a total of 100

How many chairs fit on the ends of the long table?

Answer:

2 chairs, one on each end

How many chairs fit in all? Record it on your table.

Answer:

102 chairs in all

Work with your group to determine how many chairs would fit around a very long rectangular table If 200 square tables were pushed together.

Answer:

200 chairs on each side, totaling 400, plus one on each end; grand total 402

If we let T represent the number of square tables that make one long rectangular table, what is the expression for the number of chairs that will fit around it?

Answer:

2T + 2

### Eureka Math Grade 6 Module 4 Lesson 21 Problem Set Answer Key

Question 1.

Compact discs (CDs) cost $12 each at the Music Emporium. The company charges $4. 50 for shipping and handling, regardless of how many compact discs are purchased.

a. Create a table of values that shows the relationship between the number of compact discs that Mickey buys, D, and the amount of money Mickey spends, C, in dollars.

Number of CDs Mickey Buys (D) | Total Cost in Dollars (c) |

1 | |

2 | |

3 |

Answer:

Number of CDs Mickey Buys (D) | Total Cost in Dollars (c) |

1 | $16.50 |

2 | $28.50 |

3 | $40.50 |

b. If you know how many CDs Mickey orders, can you determine how much money he spends? Write the corresponding expression.

Answer:

12D + 4.5

c. Use your expression to determine how much Mickey spent buying 8 CDs.

Answer:

8(12) + 4. 50 = 100. 50. Mickey spent $100. 50.

Question 2.

Mr. Gee’s class orders paperback books from a book club. The books cost $2.95 each. Shipping charges are set at $4. 00, regardless of the number of books purchased.

a. Create a table of values that shows the relationship between the number of books that Mr. Gee’s class buys, B, and the amount of money they spend, C, in dollars.

Number of Books Ordered (B) | Amount of Money Spent in Dollars (C) |

1 | |

2 | |

3 |

Answer:

Number of Books Ordered (B) | Amount of Money Spent in Dollars (C) |

1 | 6.95 |

2 | 9.90 |

3 | 12.85 |

b. If you know how many books Mr. Gee’s class orders, can you determine how much money they spend? Write the corresponding expression.

Answer:

2.95B + 4

c. Use your expression to determine how much Mr. Gee’s class spent buying 24 books.

Answer:

24(2.95) + 4 = 74. Mr. Gee’s class spent $74.80.

Question 3.

Sarah is saving money to take a trip to Oregon. She received $450 in graduation gifts and saves $120 per week working.

a. Write an expression that shows how much money Sarah has after working W weeks.

Answer:

450 + 120W

b. Create a table that shows the relationship between the amount of money Sarah has (M) and the number of weeks she works (W).

Amount of Money Sarah Has (M) | Number of weeks Worked (W) |

1 | |

2 | |

3 | |

4 | |

5 | |

6 | |

7 | |

8 |

Answer:

Amount of Money Sarah Has (M) | Number of weeks Worked (W) |

570 | 1 |

690 | 2 |

810 | 3 |

930 | 4 |

1,050 | 5 |

1,170 | 6 |

1,290 | 7 |

1,410 | 8 |

c. The trip will cost $1, 200. How many weeks will Sarah have to work to earn enough for the trip?

Answer:

Sarah will have to work 7 weeks to earn enough for the trip.

Question 4.

Mr. Gee’s language arts class keeps track of how many words per minute are read aloud by each of the students. They collect this oral reading fluency data each month. Below is the data they collected for one student in the first four months of school.

a. Assume this increase in oral reading fluency continues throughout the rest of the school year. Complete the table to project the reading rate for this student for the rest of the year.

Month | Number of Words Read Aloud in one Minute |

September | 126 |

October | 131 |

November | 136 |

December | 141 |

January | |

February | |

March | |

April | |

May | |

June |

Answer:

Month | Number of Words Read Aloud in one Minute |

September | 126 |

October | 131 |

November | 136 |

December | 141 |

January | 146 |

February | 151 |

March | 156 |

April | 161 |

May | 166 |

June | 171 |

b. If this increase in oral reading fluency continues throughout the rest of the school year, when would this student achieve the goal of reading 165 words per minute?

Answer:

The student will meet the goal in May.

c. The expression for this student’s oral reading fluency is 121 + 5m, where m represents the number of

months during the school year. Use this expression to determine how many words per minute the student would read after 12 months of instruction.

Answer:

The student would read 181 words per minute: 121 + 5 × 12.

Question 5.

When corn seeds germinate, they tend to grow 5 inches in the first week and then 3 inches per week for the remainder of the season. The relationship between the height (H) and the number of weeks since germination (W) is shown below.

a. Complete the missing values in the table.

Number of Weeks Since Germination (W) | Height of Corn Plant (H) |

1 | 5 |

2 | 8 |

3 | 11 |

4 | 14 |

5 | |

6 |

Answer:

Number of Weeks Since Germination (W) | Height of Corn Plant (H) |

1 | 5 |

2 | 8 |

3 | 11 |

4 | 14 |

5 | 17 |

6 | 20 |

b. The expression for this height is 2 + 3W. How tall will the corn plant be after 15 weeks of growth?

Answer:

2 + 3(15) = 47. The plant will be 47 inches tall.

Question 6.

The Honeymoon Charter Fishing Boat Company only allows newlywed couples on their sunrise trips. There is a captain, a first mate, and a deck hand manning the boat on these trips.

a. Write an expression that shows the number of people on the boat when there are C couples booked for the trip.

Answer:

3 + 2C

b. If the boat can hold a maximum of 20 people, how many couples can go on the sunrise fishing trip?

Answer:

Eight couples (16 passengers) can fit along with the 3 crew members, totaling 19 people on the boat. A ninth couple would overload the boat.

### Eureka Math Grade 6 Module 4 Lesson 21 Exit Ticket Answer Key

Krystal Klear Cell Phone Company charges $5.00 per month for service. The company also charges $0. 10 for each text message sent.

a. Complete the table below to calculate the monthly charges for various numbers of text messages sent.

Number of Text Message Sent (T) | Total Monthly Bill in Dollars |

0 | |

10 | |

20 | |

30 | |

T |

Answer:

Number of Text Message Sent (T) | Total Monthly Bill in Dollars |

0 | 5 |

10 | 6 |

20 | 7 |

30 | 8 |

T | 0.1T + 5 |

b. If Suzannah’s budget limit is $10 per month, how many text messages can she send in one month?

Answer:

Suzannah can send 50 text messages in one month for $10.