## 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

 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?
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.
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.
12D + 4.5

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