## Engage NY Eureka Math Grade 6 Module 4 End of Module Assessment Answer Key

### Eureka Math Grade 6 Module 4 End of Module Assessment Answer Key

Question 1.

Gertrude is deciding which cell phone plan is the best deal for her to buy. SuperCell charges a monthly fee of $10 and also charges $0.15 per call. She makes a note that the equation is M = 0.15C + 10, where M is the monthly charge, in dollars, and C is the number of calls placed. Global Cellular has a plan with no monthly fee but charges $0.25 per call. She makes a note that the equation is M = 0.25C, where M is the monthly charge, in dollars, and C is the number of calls placed. Both companies offer unlimited text messages.

a. Make a table for both companies showing the cost of service, M, for making from 0 to 200 calls per month. Use multiples of 20.

Answer:

b. Construct a graph for the two equations on the same graph. Use the number of calls, C, as the independent variable and the monthly charge, in dollars, M, as the dependent variable.

Answer:

c. Which cell phone plan is the best deal for Gertrude? Defend your answer with specific examples.

Answer:

The best deal depends on the number of calls placed in a month. The breakpoint is 100 calls per month. Supercell is a better deal if the number of monthly calls is less than 100. Global cellular is a better deal if the number of monthly calls is greater than 100.

Question 2.

Sadie is saving her money to buy a new pony, which costs $600. She has already saved $75. She earns $50 per week working at the stables and wonders how many weeks it will take to earn enough for a pony of her own.

a. Make a table showing the week number, W, and total savings, in dollars, S, in Sadie’s savings account.

Answer:

50w + 75

b. Show the relationship between the number of weeks and Sadie’s savings using an expression.

Answer:

If Sadie works 11 weeks, she will earn $625, which is $25 more than the cost of the pony.

Question 3.

The elevator at the local mall has a weight limit of 1,800 pounds and requires that the maximum person allowance be no more than nine people.

a. Let x represent the number of people. Write an inequality to describe the maximum allowance of people allowed in the elevator at one time.

Answer:

0 ≤ x ≤ 9

b. Draw a number line diagram to represent all possible solutions to part (a).

Answer:

c. Let w represent the amount of weight, in pounds. Write an inequality to describe the maximum weight allowance in the elevator at one time.

Answer:

0 ≤ W ≤ 1,800

d. Draw a number line to represent all possible solutions to part (c).

Answer:

Question 4.

Devin’s football team carpools for practice every week. This week is his parents’ turn to pick up team members and take them to the football field. While still staying on the roads, Devin’s parents always take the shortest route in order to save gasoline. Below is a map of their travels. Each grid line represents a street and the same distance.

Devin’s father checks his mileage and notices that he drove 18 miles between his house and Stop 3.

a. Create an equation and determine the amount of miles each gridline represents.

Answer:

Let G represent the number of grid lines passed on the map.

9G = 18

\(\frac{9G}{9}=\frac{18}{9}\)

C = 2 miles.

b. Using this information, determine how many total miles Devin’s father will travel from home to the football field, assuming he made every stop. Explain how you determined the answer.

Answer:

15 G = miles

15 (2 miles) = 30 miles

c. At the end of practice, Devin’s father dropped off team members at each stop and went back home. How many miles did Devin’s father travel altogether?

Answer:

30 G = miles

30(2 miles) = 60 miles

Question 5.

For a science experiment, Kenneth reflects a beam of a mirror. He is measuring the missing angle created when the light reflects off the mirror. (Note: The figure is not drawn to scale.)

Use an equation to determine the missing angle, labeled x in the diagram.

Answer:

A straight angle measures 180°

51° + x° + 51° = 180°

x° + 102° = 180°

x° + 102° – 102° = 180° – 102°

x° = 78°