Refer to our Texas Go Math Grade 7 Answer Key Pdf to score good marks in the exams. Test yourself by practicing the problems from Texas Go Math Grade 7 Lesson 3.3 Answer Key Markup and Markdown.

## Texas Go Math Grade 7 Lesson 3.3 Answer Key Markup and Markdown

**Example 1**

To make a profit, stores mark up the prices on the items they sell. A sports store buys skateboards from a supplier for s dollars. What is the retail price for skateboards that the manager buys for $35 and $56 after a 42% markup?

Step 1: Use a bar model.

Draw a bar for the cost of the skateboard s.

Then draw a bar that shows the markup: 42% of s, or 0.42s.

These bars together represent the cost plus the markup, s + 0.42s.

Step 2: Retail price Original cost + Markup

= s + 0.42s

= 1s + 0.42s

= 1.42s

Step 3: Use the expression to find the retail price of each skateboard.

s = $35 → Retail price = 1.42($35) = $49.70

s = $56 → Retail price = 1.42($56) = $79.52

**Reflect**

Question 1.

What If? The markup is changed to 34%; how does the expression for the retail price change?

Answer:

The expression for the retail price now looks like this:

Retail price = Original cost + Markup

= s + 0.34s

= 1 s + 0.34s

= 1.34s

Retail price = 1.34s

**Your Turn**

Question 2.

Rick buys remote control cars to resell. He applies a markup of 10%.

a. Write two expressions that represent the retail price of the cars.

Answer:

Retail price = Original cost + Markup

= s + 0.10s

= 1.10s (= 110% × s)

b. If Rick buys a remote control car for $28.00, what is his selling price?

Answer:

Using the expression above, calculate the selling price.

s = $28 ⇒ Retail price 1.10 × $28 = $30.8

Question 3.

An exclusive clothing boutique triples the price of the items it purchases for resale.

a. What is the boutique’s markup percent? ____________________________

Answer:

Let p be the markup and s the original price. The boutique triples its original price, Thus, the end price is 3s

s + p × s = 3s

1 + p = 3

p = 2 (Divide by s)

p = 200%

b. Write two expressions that represent the retail price of the clothes.

Answer:

Retail price = Original cost + Markup

= s + 2s

= 3s (= 300% × s)

**Example 2**

A discount store marks down all of its holiday merchandise by 20% off the regular selling price. Find the discounted price of decorations that regularly sell for $16 and $23.

Step 1: Use a bar model.

Draw a bar for the regular price p.

Then draw a bar that shows the discount: 20% of p, or 0.2p.

The difference between these two bars represents the price minus the discount, p – 0.2p.

Step 2: Sale price = Original price – Markdown

= p – 0.2p

= 1 p – 0.2p

= 0.8p

Step 3: Use the expression to find the sale price of each decoration.

p = $16 → Retail price = 0.8($16) = $12.80

p = $23 → Retail price = 0.8($23) = $18.40

**Reflect**

Question 4.

Conjecture Compare the single term expression for retail price after a markup from Example 1 and the single term expression for sale price after a markdown from Example 2. What do you notice about the coefficients in the two expressions?

Answer:

The first coefficient is greater than 1, and the second coefficient is lesser that 1.

**Your Turn**

Question 5.

A bicycle shop marks down each bicycle’s selling price b by 24% for a holiday sale.

a. Draw a bar model to represent the problem.

Answer:

Picture below

b. What is a single term expression for the sale price?

Answer:

Sale price = Original price – Markdown

= b – 0.24b

= 0.76b

Question 6.

Jane sells pillows. For a sale, she marks them down 5%.

a. Write two expressions that represent the sale price of the pillows.

Answer:

Retail price = Original cost – Markdown

= p – 0.05p

= 0.95p(= 95% × s)

b. If the original price of a pillow is $15.00, what ¡s the sale price?

Answer:

Using the expression above, calculate the selling price.

s = $15 ⇒ Retail price = 0.95 × $15 = $14.25

**Texas Go Math Grade 7 Lesson 3.3 Guided Practice Answer Key**

Question 1.

Dana buys dress shirts from a clothing manufacturer for s dollars each, and then sells the dress shirts in her retail clothing store at a 35% markup. (Example 1)

a. Write the markup as a decimal. __________________________________

Answer:

Markup = 35% = 0.35

b. Write an expression for the retail price of the dress shirt. _____________

Answer:

Retail price = Original cost + Markup

= s + 0.35s

= 1.35s

c. What is the retail price of a dress shirt that Dana purchased for $32.00?

Answer:

Retail price = 1.35s = 1.35 × $32 = $43.2

d. How much was added to the original price of the dress shirt? ____________

Answer:

Added price = New price – Original price

= $43.2 $32

= $11.2

**List the markup and retail price of each item. Round to two decimal places when necessary. (Example 1).**

Answer:

2.

Markup = 15% = 0.15

Retail price = Original cost + Markup

= h + 0.15h

= 1.15h

= 1.15 × $18

= $20.7

3.

Markup = 42% = 0.42

Retail price = Original cost + Markup

= b + 0.42b

= 1.42b

= 1.42 × $22.50

= $31.95

4.

Markup = 75% = 0.75

Retail price = Original cost + Markup

= s + 0.75s

= 1.75s

= 1.75 × $33.75

≈ $59.06

5.

Markup = 33% = 0.33

Retail price = Original cost + Markup

= s + 0.33s

= 1.33s

= 1.33 × $74.99

≈ $99.74

6.

Markup = 100% = 1

Retail price = Original cost + Markup

= c + 1 c

= 2c

= 2 × $48.60

= $97.20

7.

Markup = 125% = 1.25

Retail price = Original cost + Markup

= p + 1.25p

= 2.25p

= 2.25 × $185

= $416.25

**Find the sale price of each item. Round to two decimal places when necessary. (Example 2)**

Question 8.

Original price: $45.00; Markdown: 22%

Answer:

Markdown = 22% = 0.22

Sale price = Original cost Iarkdown

= x – 0.22x

= 0.78x

= 0.78 × $45

= $35.1

Question 9.

Original price: $89.00; Markdown: 33

Answer:

Markdown = 33% = 0.33

Sale price = Original cost – Markdown

= x – 0.33x

= 0.67x

= 0.67 × $89

= $59.63

Question 10.

Original price: $23.99; Markdown: 44%

Answer:

Markdown = 44% = 0.44

Sale price = Original cost – Markdown

= x – 0.44x

= 0.56x

= 0.56 × $23.99

≈ $13.43

Question 11.

Original price: $279.99, Markdown: 75%

Answer:

riarkdown = 75% = 0.75

Sale price = Original cost – Markdown

= x – 0.75x

= 0.25x

= 0.25 × $279.99

≈ $70

**Essential Question Check: In**

Question 12.

How can you determine the sale price if you are given the regular price and the percent of markdown?

Answer:

First, write markdown as a decimal. Then, write the expression for the Sale price by subtracting markdown multiplied by the original price from the original price.

**Texas Go Math Grade 7 Lesson 3.3 Independent Practice Answer Key**

Question 13.

A bookstore manager marks down the price of older hardcover books, which originally sell for b dollars, by 46%.

a. Write the markdown as a decimal. _______________________________

Answer:

Markdown = 46% = 0.46

b. Write an expression for the sale price of the hardcover book. ______________

Answer:

Sale price = Original cost – Markdown

= b – 0.46b

= 0.54b

c. What is the sale price of a hardcover book for which the original retail price was $29.00? _______________________________

Answer:

Sale price = 0.54b

= 0.54 × $29

= $15.66

d. If you buy the book in part c, how much do you save by paying the sale price? ______________

Answer:

Money saved = Original price – Sale price

= $29 – $15.66

= $13.34

Question 14.

Raquela’s coworker made price tags for several items that are to be marked down by 35%. Match each Regular Price to the correct Sale Price, if possible. Not all sales tags match an item.

Answer:

Markdown = 35% = 0.35

Sale price = Regular price – Markdown

= x – 0.35x

= 0.65x

Now, calcuLate each price separately and match.

Sale price = 0.65x

= 0.65 × $3.29

≈ $2.14

Sale price = 0.65x

= 0.65 × $4.19

= $2.72

Sale price = 0.65x

= 0.65 × $2.79

≈ $1.81

Sale price = 0.65x

= 0.65 × $3.09

≈ $2.01

Sale price = 0.65x

= 0.65 × $3.77

≈ $2.45

Question 15.

**Communicate Mathematical Ideas** For each situation, give an example that includes the original price and final price after markup or markdown.

Answer:

We are going to rise the same Original price for all 3 subtasks.

Original price = x = $100

a. A markdown that is greater than 99% but less than 100%

Answer:

Markdown = 99.5% = 0.995

Sale price = x – 0.995x

= 0.005%

= 0.005 × $100

= $0.5

b. A markdown that is less than 1%

Answer:

Markdown = 0.5% = 0.005

Sale price = x – 0.005x

= 0.995x

= 0.995 × $100 = $99.5

c. A markup that is more than 200%

Answer:

Markdown = 250% = 2.5

Sale price = x + 2.5x

= 3.5x

= 3.5 × $100 = $350

Question 16.

**Represent Real-World Problems** Harold works at a men’s clothing store, which marks up its retail clothing by 27%. The store purchases pants for $74.00, suit jackets for $325.00, and dress shirts for $48.00. How much will Harold charge a customer for two pairs of pants, three dress shirts, and a suit jacket?

Answer:

First, get the expression for Retail, price.

Retail price = Original cost + Markup

= x + 27%x

= x + 0.27x

= 1.27x

Using the expression for RetaiL price, calculate the prices of given items.

Pants Retail price = 1.27 × .874

= $93.98

Suit jackets Retail price = 1.27 × $325

= $412.75

Dress shirts Retail price = 1.27 × $48

= $60.96

Calculate the bill of the customer using the obtained Retail prices.

2 pairs of pants + 3 dress shirts + 1 suit jacket = 2 × $93.98 + 3 × $60.96 + $412.75

= $187.96 + $182.88 + $412.75

= $783.59

Question 17.

**Analyze Relationships** Your family needs a set of 4 tires. Which of the following deals would you prefer? Explain.

(I) Buy 3, get one free (II) 20% off (III) \(\frac{1}{4}\) off

Answer:

(I)

If you buy 3 and get 1 free, you pay \(\frac{3}{4}\) of the price, that means you get \(\frac{1}{4}\) discount

(II)

20% = 0.2 = \(\frac{1}{5}\)

It is obvious that options (I) and (III) are the same, and they are born preferrable over option (II).

**H.O.T. Focus On Higher Order Thinking**

Question 18.

**Critique Reasoning** Margo purchases bulk teas from a warehouse and marks up those prices by 20% for retail sale. When teas go unsold for more than two months, Margo marks down the retail price by 20%. She says that she is breaking even, that is, she is getting the same price for the tea that she paid for it. Is she correct? Explain.

Answer:

No, she is not correct. When she is applying markup of 20%, the Retail price is 120% of the original price. Let x be the original price, Retail price = 1.2x.

Now, calculate the Retail price marked down by 20%. Let r be the Retail price and in the marked down price.

m = r – 0.2r

= 0.8r

= 0.8 × 1.2x

= 0.96x

As you can see, she is not breaking even, she is losing 4% of income on tea that goes unsold for 2 months.

Question 19.

**Problem Solving** Grady marks down some $2.49 pens to $1.99 for a week and then marks them back up to $2.49. Find the percent of increase and the percent of decrease to the nearest tenth. Are the percents of change the same for both price changes? If not, which is a greater change?

Answer:

First, find the markdown by finding the Amount of change, and dividing it by the Original cost.

Amount of change = $2.49 – $1.99

= $0.5

Markdown = \(\frac{\$ 0.5}{\$ 2.49}\)

≈ 0.201

≈ 20.1%

Now, find the markup by dividing the amount of change (which is the same) by the Marked down cost

Markup = \(\frac{\$ 0.5}{\$ 1.99}\)

≈ 0.251

≈ 25.1%

It is obvious that the Markup is greater than the Markdown by ≈ 5%.

Question 20.

**Persevere in Problem Solving** At Danielle’s clothing boutique, if an item does not sell for eight weeks, she marks it down by 15%. If it remains unsold after that, she marks it down an additional 5% each week until she can no longer make a profit. Then she donates it to charity.

Rafael wants to buy a coat originally priced $150, but he can’t afford more than $110. If Danielle paid $100 for the coat, during which week(s) could Rafael buy the coat within his budget? Justify your answer.

Answer:

First, apply 15% markdown to get the price after 8 weeks. ‘Then, keep applying 5% markup, until you get the price higher than $100 and lower than $110. Bemuse the coat goes to charity after that. but the coat has to be within the budget.

Price during 9th week = $150 – $150 × 0.13 = $127.5

Price during 10th week = $127.5 – $127.5 × 0.05 = $121.13

Price during 11th week = $121.13 – $121.13 × 0.05 = $115.08

Price during 12th week = $115.08 – $115.08 × 0.05 = $109.33

Price during 13th week = $109.33 – $109.33 × 0.05 = $103.86

Price during 14th week = $103.86 – $103.86 × 0.05 = $99.67

Rafael could buy the coat during 12th and 13th week within his budget.