We included**HMH Into Math Grade 7 Answer KeyPDF****Module 7 Lesson 1 Write Linear Expressions in Different Forms of Situations **to make students experts in learning maths.

I Can write different forms of linear expressions to represent the same real-world situation.

**Spark Your Learning**

A bus driver has students going on a field trip enter the bus in pairs. He fills one row of the bus at a time, front to back. Write a rule that shows the total number of people on the bus after any number of rows is filled. Let the bus driver’s seat count as Row 1.

Answer:

4x – 3

Explanation:

A rule that shows the total number of people on the bus after any number of rows is filled with 4x – 3.

**Turn and Talk** How would your rule change if the second row of each bus only sat 2 students to make room for a wheelchair?

Answer:

**Build Understanding**

Question 1.

Henry is remodeling a kitchen and needs some wiring installed for additional outlets and lighting. An electrician provides him an estimate which includes a one-time service fee plus an hourly rate, as shown, to complete the wiring.

A. What is the unknown value in this situation?

Answer:

The number of additional lights and outlets henry plans to install.

B. What might you use to represent the unknown value in this situation?

Answer:

I use an additional light fee to represent the unknown value in this situation.

C. Write an expression that would represent the total charges.

Answer:

Total charges = Service fee + hourly rate + additional lights and outlets fee

D. Electricians who work on Saturday earn time and a half. That means the pay is 1.5 times the normal hourly rate for each hour. Write expressions to represent pay earned on a Saturday in two different ways.

Answer:

E. The electrician decides to bring an apprentice on the job, so they split the hourly rate paid by the customer. The electrician takes a reduced hourly wage of $40, and pays the apprentice the remaining $14.50 per hour. Write an expression that models how the total charges are shared.

Answer:

F. Are the expressions in Parts C and E equivalent? Why?

Answer:

**Turn and Talk** Why is it useful to represent an amount with a variable in real-world models?

Answer:

Question 2.

A department store is offering a promotion on candles as shown. Rhonda is buying three candles at the same original price for a birthday present.

A. What is the unknown value in this situation, and what could you use to represent the unknown?

Answer:

B. The third candle is discounted. Find the percent of the original price of the candle Rhonda would be paying, and explain your reasoning.

Answer:

C. Write an expression for the total cost before tax in relation to the cost of the first two candles and the cost of the discounted candle.

Answer:

D. Is there another way to write the total cost expression? If so, write the expression and explain why the expressions are equivalent.

Answer:

**Turn and Talk** What other equivalent expressions could you write to represent the total cost of the candles?

Answer:

**Check Understanding**

Question 1.

Abigail’s parents pay her $5 an hour for weeding the yard and pay her little sister $3 an hour for raking leaves. Write an expression in two different ways to represent the amount her parents will pay Abigail and her sister for working the same number of hours.

Answer:

5h + 3h

Explanation:

Abigail’s parents pay $5 an hour for the weeding.

Her little sister $3 an hour for raking leaves.

The amount her parents will pay Abigail and her sister for working the same number of hours is $5h + $3h.

Question 2.

Juice is on sale with the rule “buy one, get one half-off.” Write an expression in two different ways to represent the cost of buying two containers of juice on sale.

Answer:

0.5 j + j

Explanation:

An expression in two different ways to represent the cost of buying two containers of juice on sale is 0.5 j + j.

**On Your Own**

Question 3.**Use Structure** A wedding photographer and an assistant work together to photograph weddings. The rates are shown in the advertisem*nt. Write an expression to represent the total cost for photography at a wedding in two different ways.

Answer:

Question 4.**Use Structure** Benita buys 2 shirts for the same price. The sales tax rate is 6.5%. Write an expression to represent the total cost for the shirts in two different ways.

Answer:

2S + 0.065(2S)

Explanation:

An expression to represent the total cost for the shirts in two different ways is 2S + 0.065(2S).

Question 5.**Use Structure** A hobby store is having a promotion on picture frames: buy 3 get the 4th frame at 75% off. Write an expression to represent the total cost for 4 frames in two different ways.

Answer:

3x + (x-0.75x)4x – 0.75x

Explanation:

Let x is the cost of the frame.

3x + (x-0.75x)4x – 0.75x

**For Problems 6-7, decide whether the expressions are equivalent and write yes or no. If no, write an expression that is equivalent to the first one.**

Question 6.

k + 0.10k and 1.1k

Answer:

2.10k

Explanation:

Let us solve the given expression

k + 0.10k + 1.1k

2.10k

Question 7.

2m – 0.2m and 2.2m

Answer:

4m

Explanation:

Let us solve the given equation

The given equation is 2m – 0.2m and 2.2m

2m + 2.2m -0.2m

4.2m -0.2m

4m.

Question 8.**Open-Ended** Write an expression equivalent to 0.65b.

Answer:

0.60b + 0.05b

Question 9.**Open-Ended** Write an expression equivalent to 22 – 0.58y.

Answer:

20 + 2 -0.50y + 0.08y

**I’m in a Learning Mindset!**

What about writing linear expressions causes a fixed-mindset voice in my head? What can I do about it?

Answer:

**Lesson 7.1 More Practice/Homework**

Question 1.**Use Structure** A plumber charges a customer a one-time service fee of $79, $62 per hour for labor, and a surcharge of $15 per hour due to the call being an emergency. Write an expression to represent the total charges for the plumber in two different ways.

Answer:

79 + 62x + 15x

Explanation:

Let x be the number of hours the plumber has worked.

So the total charge is represented by

79 + 62x + 15x.

Question 2.**Use Structure** Mia buys ink at the office supply store for a business. She buys 3 printer cartridges, and the sales tax is 7%. Write an expression to represent the total cost of ink supplies in two different ways.

Answer:

An equation to represent the total cost of 2 different ones is $25.68.

Explanation:

Given,

The number of printer cartridges bought is 3.

Sales tax = 7%

Now assume the cost of each beach printer cartridge = $12

Total cost = $12 × 3

= $36

Amount of tax = 7% of $36

= 0.07 × 36

= $2.52

Amount paid = $2.52 + $36

$38.52

An expression to represent the total cost of ink supplies in two different ones = 7% × (12 × 2) + 24

= 0.07 × 24 + 24

= $1.68 + 24

= $ 25.68

Question 3.**Use Structure** Emilio buys liter bottles of shampoo when the store has the promotion shown. Write an expression in two different ways to represent the total cost of 3 liters of shampoo.

Answer:

Question 4.**Reason** Maribelle uses x yards of material to make a quilt. A customer requests 5 quilts that are 20% larger than the normal pattern. Write an expression to represent the total yards of material needed for the requested quilts in two different ways.

Answer:

f(x) = 6x

Explanation:

Let the total yards of material is f(x)

f(x) = 5 ( x × (1 + 20%))

= 5 ( x × (1 + (\(\frac{20}{100}\)))

= 5 ( x × (\(\frac{6}{5}\)))

= 6x

Question 5.**Use Structure** Gavin works two part-time jobs to pay for college. He works 8 hours each week tutoring and 10 hours each week in the dining hall. He gets paid the same hourly wage at each job. His parents also provide Gavin $50 per week for expenses. Gavin writes this expression,18w + 50, where w represents his hourly wage, to represent his total weekly income. Write another expression equivalent to Gavin’s.

Answer:

8w + 10w + 50

Explanation:

The total weekly income is 8w + 10w + 50.

8w is the money for tutoring

10w is the money from the dining hall.

So the answer is 8w + 10w + 50.

**For Problems 6-9, decide whether the expressions are equivalent and write yes or no.**

Question 6.

3n + 4n + 1 + 2n – 3 and 9n – 2

Answer:

18n – 4

Explanation:

Let us solve the given expression

3n + 4n + 1 + 2n – 3 + 9n – 2

3n + 4n + 2n + 9n + 1 – 3 – 2

7n + 2n + 9n + 1 – 5

9n + 9n – 4

18n – 4

Question 7.

3.1b – 0.22b and 2.88b

Answer:

5.76b

Explanation:

Let us solve the given expression

3.1b + 2.88b – 0.22b

5.98b – 0.22b

5.76b

Question 8.

13x – 7x + 4 and 20x + 4

Answer:

26x + 8

Explanation:

Let us solve the given question

The given expression is 13x – 7x + 4 and 20x + 4

13x + 20x -7x + 4 + 4

33x – 7x + 8

26x + 8

Question 9.

18 + 3.1m + 4.21m – 2 and 16 + 7.31m

Answer:

14.61m + 32.

Explanation:

Let us solve the given equation

18 + 3.1m + 4.21m – 2 and 16 + 7.31m

18 + 16 – 2 + 3.1m + 4.21m + 7.31m

34 – 2 + 7.31m + 7.31m

32 +14.61m

**Test Prep**

Question 10.

Students running a food drive have collected their goal amount of canned goods. Over the weekend, volunteers collect an additional 18% of the goal. Write an expression to represent the total percent of their goal collected in two different ways.

Answer:

11800%

Explanation:

From the given question find

100 × (1 + 18%)

Calculate the sum 100 × 1.18 = 118

Multiply by 100 to both numerator and denominator

118 × \(\frac{100}{100}\)

Find the product

\(\frac{11800}{100}\)

Write this in percentage

118%

Question 11.

A bookstore has a bargain table where every book is the same price. In addition, the bookstore gives 20% off every 5th book purchased from the bargain table. Write an expression to represent the total cost of purchasing 5 books in two different ways.

Answer:

The expression to represent the total cost of purchasing 5 books in two different ways is 4.

Explanation:

From the given conditions

Calculate 5 × (1 – 20%)

Calculate the sum or differene 5 × (1 – \(\frac{20}{100}\))

= 5 × (1 – \(\frac{1}{5}\))

= 5 × (\(\frac{4}{5}\))

= 5 × (0.8)

= 4

Question 12.

A restaurant offers a dinner special for $25 per person plus a $5-per-person tip. Select all the expressions that represent the total cost of the special for m people.

(A) 25m + 5m

(B) 25 m – 5m

(C) 30 m

(D) 25 + 5m

(E) 25m + 5

Answer:

25m + 5m

30m

Explanation:

Dinner per person is $25.

Per-person tip is $5.

Cost of the special for m people is

25m + 5m

30m

Question 13.

Leon orders sheets of metal for an art class he teaches. He needs 12 sheets for his Tuesday night class and 8 sheets for his Thursday night class. There is also a $7.95 delivery fee. Select all the expressions that represent the total cost of Leon’s order, if x is the cost of one sheet.

(A) 12x + 8x

(B) 12x + 8x + 7.95

(C) 20x + 7.95

(D) 12x + 8x – 7.95

(E) 12x + 8x + 7.95x

Answer:

(B) 12x + 8x + 7.95

(A) 12x + 8x

Expalantion:

Cost of one sheet is x.

He needs 12 sheets for his Tuesday night class.

8 sheets for his Thursday night class.

delivery fee is $7.95.

The expressions that represent the total cost of Leon’s order is

12x + 8x + 7.95

12x + 8x

**Spiral Review**

Question 14.

Henri paid $10.75 for a calculator, $4.98 for copier paper, and $3.21 for folders. He paid with a $20 bill and got $1.06 in change. Show by using estimation that Henri’s change is reasonable.

Answer:

$10.75 + $4.98 + $3.21 = $18.94

He paid a bill of $20 bill and got a change of $1.06

$20 – $1.06 = $18.94

Therefore Henri’s change is reasonable.

Question 15.

What are the common factors of 6, 9, and 18?

Answer:

1, 3

Explanation:

The common factors of 6, 9, and 18 are 1, 3.