We included **HMH Into Math Grade 8 Answer Key**** PDF** **Module 3 Solve Linear Equations **to make students experts in learning maths.

## HMH Into Math Grade 8 Module 3 Answer Key Solve Linear Equations

**Entrepreneur**

An entrepreneur is a person who starts and operates a business. Entrepreneurs recognize the need or desire for a product or service that is not currently available and then set out to provide it. An entrepreneurâ€™s skills may vary depending on the business, but all entrepreneurs need resilience and perseveranceâ€”a new business is bound to have ups and downs. Entrepreneurs must expect setbacks and be prepared to keep going in spite of them.

**Stem Task:**

Gina’s part-time computer repair business is growing. The table shows her approximate earnings each month. Predict when her monthly earnings will reach $1000 if her earnings continue to increase at a constant rate. Explain your thinking

Answer:

Her earnings increase every month by $40.

In the first month, she earns $600

In second month, she earns $40 more = $600 + $40 = $640

In the third month, she earns $40 more = $640 + $40 = $680

In the fourth month, she earns = $680 + $40 = $720

In the fifth month, she earns = $720 + $40 = $760

In the sixth month, she earns = $760 + $40 = 800 and so on…

every year she is increasing her earnings by $40 more constantly.

**Learning Mindset!**

**Perseverance Checks for Understanding**

Perseverance is a quality that allows you to keep working toward a goal, even when you are faced with difficulties or delays. Projects and tasks that are long or complex can challenge your perseverance. Here are some tips to help you persevere and not give up on your goal.

- Check your progress often to be sure you’re on the right path. Identify steps and milestones that will let you track your progress. Are you moving closer to your goal?
- Before moving forward from a setback, look back. What caused the setback? What can you learn from it? Is there anything you can do differently in the future to prevent the setback from happening again?
- Don’t give up, but don’t be afraid to adjust your goals or plans either. Your situation may change, or you may encounter new and interesting ideas that you weren’t aware of when you started.

**Reflect**

Question.

What strategies did you use to complete the STEM Task? Did you try any strategies that did not work? If so, how did you adjust?

Answer:

– Define the problem.

– Visualize the problem

– Draw the diagram of the problem

– Break the problem into smaller pieces

– Redefine the problem

– Collect and organize the information about the problem

– Consider the trial-and-error approach

Question.

What can you learn by describing your strategies for completing a task or solving a problem? What can you learn by listening to others’ strategies?

Answer:

– Understanding how a variety of problem-solving strategies work is important because different problems typically require you to approach them in different ways to find the best solution. By mastering several problem-solving strategies, you can more effectively select the right plan of action when faced with challenges in the future.

**Rent a Tent**

Four friends went camping but they couldnâ€™t stay the same number of days. They each rented different types of tents, but each paid a total of $27. The cost of each tent rental is represented by an equation.

Solve for d to find the number of days each person camped. The constant represents the companyâ€™s charge to clean the tent.

Kateâ€™s rental: __8d + 3 = 27__ Andreaâ€™s rental: __11d + 5 = 27__

Days spent camping ____ Days spent camping _____

Manuelâ€™s rental: __7.5d + 4.5 = 27__ Peterâ€™s rental: __8.5d + 1.5 = 27__

Days spent camping ____ Days spent camping ____

**Turn and Talk**

- Explain how to solve each equation to find the number of days.

Answer:

(1) : Kate’s rental equation: 8d + 3 = 27

simplifying the equation:

8d = 27 – 3

8d = 24

d = 24/8

d = 3

(2): Andrea’s rental equation: 11d + 5 = 27

simplifying the equation:

11d = 27 – 5

11d = 22

d = 22/11

d = 2

(3): Manuel’s rental equation: 7.5d + 4.5 = 27

simplifying the equation:

7.5d = 27 – 4.5

7.5d = 22.5

d = 22.5/7.5

d = 3

(4): Peter’s rental equation: 8.5d + 1.5 = 27

simplifying the equation:

8.5d = 27 – 1.5

8.5d = 25.5

d = 25.5/8.5

d = 3 - If you rent a tent for 5 days the cleaning fee is not charged. Which tent costs the least to rent for 5 days? Explain.

**Are You Ready?**

**Complete these problems to review prior concepts and skills you will need for this module.**

**Solve One-Step Equations**

**For Problems 1-3, solve each equation.**

Question 1.

x + 24 = 70

________

Answer:

The above-given equation:

x + 24 = 70

Get all like terms on one side

x = 70 – 24

x = 46

Question 2.

b – 3.5 = 6.8

________

Answer:

The above-given equation:

b – 3.5 = 6.8

get all like terms on one side

b = 6.8 + 3.5

b = 10.3

Question 3.

\(\frac{t}{8}\) = 4

________

Answer:

The above-given equation:

t/8 = 4

Multiply both sides by 8

8 * (t/8) = 4 * 8

t = 32

Question 4.

It costs $0.80 to download a song from an online music store. Maxine has $6.00 to spend on songs. The equation 0.80s = 6.00 can be used to determine the number of songs s that she can afford to download. Solve the equation, and interpret the solution.

Answer:

The cost of each song download = $0.80

The amount Maxine spends on songs = $6.00

The above-given equation:

0.80s = 6.00

s = 6/0.8

s = 7.5

**Write and Solve Two-Step Equations**

**For Problems 5-10, solve each equation.**

Question 5.

4a – 12 = -8

Answer:

The above-given equation:

4a – 12 = -8

get like terms on one side

4a = -8 + 12

4a = 4

a = 4/4

a = 1

Question 6.

\(\frac{n}{4}\) + 15 = 38

Answer:

The above-given equation:

n/4 + 15 = 38

get like terms on one side

n/4 = 38 – 15

n/4 = 23

n = 23 x 4

n = 92

Question 7.

2r + 10 = 14

___________

Answer:

The above-given equation:

2r + 10 = 14

get like terms on one side

2r = 14 – 10

2r = 4

r = 4/2

r = 2

Question 8.

\(\frac{x}{3}\) – 5 = -3

___________

Answer:

The above-given equation:

x/3 – 5 = -3

get like terms on one side

x/3 = -3 + 5

x/3 = 2

x = 2 * 3

x = 6

Question 9.

2p = 47 – 17

Answer:

The above-given equation:

2p = 47 – 17

2p = 30

p = 30/2

p = 15

Question 10.

\(\frac{z}{2}\) = 13 + 3

___________

Answer:

The above-given equation:

z/2 = 13 + 3

z/2 = 16

z = 16 * 2

z = 32

Question 11.

A one-year membership to a swim club is $170. This cost includes a $20 registration fee and 12 monthly payments. The equation 12m + 20 = 170 can be used to find the amount m of each monthly payment. Solve the equation, and interpret the solution.

Answer:

The above-given equation:

12m + 20 = 170

12m = 170 – 20

12m = 150

m = 150/12

m = 12.5

Question 12.

A group of friends bought 6 movie tickets. They used a coupon for $2.00 off the cost of one of the tickets, and their total cost with the coupon was $50.50. Write an equation that can be used to determine the regular cost of each movie ticket.

Answer:

The total cost of the 6 movie tickets = (6 x the cost of each ticket) – the value of one coupon

The equation is:

50.50 = 6c – $2

Flip the equation

6c – $2 = 50.50

add 2 to the both sides

6c – 2 + 2 = 50.50 + 2

6c = 52.5

c = 52.5/6

c = 8.75

Therefore, the regular cost of each movie ticket is $8.75

Question 13.

Shaun keeps his baseball card collection in an album. The album has 25 pages, and each page can hold 9 cards. Four pages are empty, and the rest are full. Write an equation that can be used to determine the number of baseball cards b in Shaunâ€™s collection.

Answer:

Number of pages in the album = 25

pages Number of empty pages= 4

Number of full pages= 25 pages – 4 pages = 21 pages.

Number of cards that each page can hold = 9 cards .

The equation to determine the number of baseball cards in Shaun’s collection is

b = (25 – 4) Ã— 9

b = 21 x 9

b = 189