MODELING ALGEBRAIC EXPRESSIONS WORKSHEETS

Questions 1-4 : Use a bar model to represent the following expressions.

Question 1 :

7 + x

Question 2 :

z/3

Question 3 :

t - 2

Question 4 :

4y

Question 5 :

Katrina and Andrew started the day with the same amount of money. Katrina spent 5 dollars on lunch. Andrew spent 3 dollars on lunch and 2 dollars on a snack after school. Do Katrina and Andrew have the same amount of money left ?

Question 6 :

On a math quiz, Tina scored 3 points more than Julia. Juan scored 2 points more than Julia and earned 2 points in extra credit. Write an expression and draw a bar model to represent Tina’s score and Juan’s score. Did Tina and Juan make the same grade on the quiz ? Explain.

Question 7 :

Paloma works part-time, 4 hours per day, selling fitness club memberships. She is paid $9/h, plus a $12 commission for each 1-year membership she sells.

a) Write an algebraic expression that describes Paloma’s total earnings.

b) Find the amount Paloma makes in 8 hours when she sells 7 memberships.

c) How many memberships does Paloma need to sell to earn $600 in a 24 hour work week?

Question 8 :

The mass of a banana plus its peel is 360g. The mass of the banana is four times the mass of the peel. What is the mass of the peel?

Question 9 :

A wire is (7x – 3) metres long. A length of (3x – 4) metres is cut for use. Now, answer the following questions :

(a) How much wire is left?

(b) If this left out wire is used for making an equilateral triangle. What is the length of each side of the triangle so formed?

Question 10 :

The length of a side of square is given as 2x + 3. Which expression represents the perimeter of the square?

(a) 2x + 16     (b) 6x + 9     (c) 8x + 3     (d) 8x + 12

Question 11 :

Find the simplest expression for the shaded area of each figure

1. Answer :

7 + x

2. Answer :

z/3

3. Answer :

t - 2

4. Answer :

4y

5. Answer :

Let x be the money that Katrina and Andrew had at the beginning. 

Step 1 :

Write an algebraic expression to represent the money Katrina has left.

x - 5

Represent the expression with a model.

Step 2 :

Write an algebraic expression to represent the money Andrew has left.

x - 3 - 2

Represent the expression with a model.

Step 3 :

Compare the models.

The models are equivalent, so the expressions are equivalent.

Andrew and Katrina have the same amount of money left.

6. Answer :

Let y be the points scored by Julia. 

Step 1 :

Write an algebraic expression to represent the points scored by Tina.

y + 3

Represent the expression with a model.

Step 2 :

Write an algebraic expression to represent the points scored by Juan.

y + 2 + 2

Represent the expression with a model.

Step 3 :

Compare the models.

The models are not equivalent, so the expressions are not equivalent.

Hence, Tina and Juan did not make the same grade on the quiz.

7. Answer :

Earning per hour = $9

Commission for 1 year membership that he sells = $12

Let x be the number of membership he sells.

Number of hours he is working = 4

a)

Total earning = 4(9) + 12x

= 36 + 12x 

b) 

When he is working for 8 hours and sells 7 memberships

= 8(9) + 12(7)

= 72 + 84

= 156

c)

Number of hours he is working = 24

Amount earns = 600

9(24) + 12x = 600

216 + 12x = 600

12x = 600 - 216

12x = 384

x = 384/12

x = 32

So, the number of memberships is 32.

8. Answer :

Mass of banana + weight of its peel = 360 g

Mass of banana = 4(mass of peel)

Let x be the mass of peel.

4x + x = 360

5x = 360

x = 360/5

x = 72

Mass of peel = 72 grams.

9. Answer :

Length of wire = 7x – 3 metres

Length of wire cut = 3x - 4

a) quantity of wire left = 7x - 3 - (3x - 4)

= 7x - 3 - 3x + 4

= 4x + 1

(b) Length of equilateral triangle = 4x + 1

Side length of equilateral triangle = (4x + 1)/3

10. Answer :

Side length of square = 2x + 3

Perimeter of square = 4(side length)

= 4 (2x + 3)

= 8x + 12

So, the required perimeter is 8x + 12 meters

11. Answer :

Side length of large square = 2x + 1

Side length of small square =x - 5

Area of shaded region = (2x + 1)² - (x - 5)²

= (2x)² + 2(2x)(1) + 1² - (x² - 2x(5) + 5²)

= 4x² + 4x + 1 - (x² - 10x + 25)

= 4x² + 4x + 1 - x² + 10x - 25

= 4x² - x² + 4x + 10x + 1 - 25

= 3x² + 14x - 24

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