Engage NY Eureka Math 7th Grade Module 2 Lesson 18 Answer Key
Eureka Math Grade 7 Module 2 Lesson 18 Exercise Answer Key
Exercise 1.
John’s father asked him to compare several different cell phone plans and identify which plan will be the least expensive for the family. Each phone company charges a monthly fee, but this fee does not cover any services: phone lines, texting, or internet access. Use the information contained in the table below to answer the following questions.
Cell Phone Plans
All members of the family may not want identical plans; therefore, we will let x represent the number of phone lines, y represent the number of phone lines with unlimited texting, and z represent the number of phone lines with internet access.
Expression
Company A __
Company B __
Company C ___
Answer:
Company A 70 + 20x + 15y + 15z
Company B 90 + 15x + 10y + 20z
Company C 200 + 10x
Using the expressions above, find the cost to the family of each company’s phone plan if:
a. Four people want a phone line, four people want unlimited texting, and the family needs two internet lines.
Answer:
Which cell phone company should John’s family use? Why?
Answer:
The family should choose Company B since it is cheaper than the others for the given values
b. Four people want a phone line, four people want unlimited texting, and all four people want internet lines.
Answer:
Which cell phone company should John’s family use? Why?
Answer:
The family should choose Company C since it is cheaper than the other companies for the given values.
c. Two people want a phone line, two people want unlimited texting, and the family needs two internet lines.
Answer:
Which cell phone company should John’s family use? Why?
Answer:
The family should choose Company A since it is cheaper than the other companies for the given values.
Exercise 2.
Three friends went to the movies. Each purchased a medium – sized popcorn for p dollars and a small soft drink for s dollars.
a. Write the expression that represents the total amount of money (in dollars) the three friends spent at the concession stand.
Answer:
3(p + s)
b. If the concession stand charges $6.50 for a medium – sized popcorn and $4.00 for a small soft drink, how much did the three friends spend on their refreshments altogether?
Answer:
One possible solution is shown here; more solution methods are shown in the discussion that follows.
3(p + s)
3(6.50 + 4)
3(10.50)
31.50
They spent $31.50.
Exercise 3.
Complete the table below by writing equivalent expressions to the given expression and evaluating each expression with the given values.
Answer:
Eureka Math Grade 7 Module 2 Lesson 18 Problem Set Answer Key
Question 1.
Sally is paid a fixed amount of money to walk her neighbor’s dog every day after school. When she is paid each month, she puts aside $20 to spend and saves the remaining amount. Write an expression that represents the amount Sally will save in 6 months if she earns m dollars each month. If Sally is paid $65 each month, how much will she save in 6 months?
Answer:
m= monthly pay
6(m – 20)
6m – 120
For m=65
6(m – 20)
6(65 – 20)
6(45)
270
or
6(m – 20)
6(65 – 20)
390 – 120
270
Sally will save $270 in 6 months.
Question 2.
A football team scored 3 touchdowns, 3 extra points, and 4 field goals.
a. Write an expression to represent the total points the football team scored.
Answer:
t= number of points for a touchdown.
e= number of points for the extra point.
f= number of points for a field goal.
3t + 3e + 4f
b. Write another expression that is equivalent to the one written above.
Answer:
Answers may vary. Sample response: 3t + 3e + 2f + 2f
c. If each touchdown is worth 6 points, each extra point is 1 point, and each field goal is 3 points, how many total points did the team score?
Answer:
3t + 3e + 4f
3(6) + 3(1) + 4(3)
18 + 3 + 12
33
Question 3.
Write three other expressions that are equivalent to 8x – 12.
Answer:
Answers may vary.
4(2x – 3)
6x + 2x – 12
8(x – 1) – 4
– 12 + 8x
Question 4.
Profit is defined as earnings less expenses (earnings – expenses). At the local hot – air balloon festival, the Ma & Pops Ice Cream Truck sells ice cream pops, which cost them $0.75 each but are sold for $2 each. They also paid $50 to the festival’s organizers for a vendor permit. The table below shows the earnings, expenses, and profit earned when 50, 75, and 100 ice cream pops were sold at the festival.
a. Write an expression that represents the profit (in dollars) Ma & Pops earned by selling ice cream pops at the festival.
Answer:
p represents the number of pops sold.
2p – 0.75p – 50
b. Write an equivalent expression.
Answer:
1.25p – 50
c. How much of a profit did Ma & Pops Ice Cream Truck make if it sold 20 ice cream pops? What does this mean? Explain why this might be the case.
Answer:
1.25p – 50
1.25(20) – 50
25 – 50
– 25
They did not make any money; they lost $25. A possible reason is it could have been cold or rainy and people were not buying ice cream.
d. How much of a profit did Ma & Pops Ice Cream Truck make if it sold 75 ice cream pops? What does this mean? Explain why this might be the case.
Answer:
1.25p – 50
1.25(75) – 50
93.75 – 50
43.75
They made a profit of $43.75. Possible reasons are the weather could have been warmer and people bought the ice cream, or people just like to eat ice cream no matter what the weather is.
Eureka Math Grade 7 Module 2 Lesson 18 Exit Ticket Answer Key
Bradley and Louie are roommates at college. At the beginning of the semester, they each paid a security deposit of A dollars. When they move out, their landlord will deduct from this deposit any expenses (B) for excessive wear and tear and refund the remaining amount. Bradley and Louie will share the expenses equally.
→ Write an expression that describes the amount each roommate will receive from the landlord when the lease expires.
→ Evaluate the expression using the following information: Each roommate paid a $125 deposit, and the landlord deducted $50 total for damages.
Answer:
Deposit each person paid: A
Total damages: B
Each roommate receives: A – \(\frac{B}{2}\)
A=125, B=50
A – \(\frac{B}{2}\)
125 – \(\frac{50}{2}\)
125 – 25
100