## Simplifying and Evaluating Algebraic Expressions

#### 1. There are *p* pencils in one box. Rayan has 6 boxes of pencils and Amelia has 4 boxes of pencils.

a) How many pencils do they have altogether in terms of *p*?

b) How many more pencils has Rayan than Amelia in terms of *p*?

c) If each box has 6 pencils, how many more pencils has Rayan than Amelia?

a) Rayan has 6 boxes of pencils. Each box has

Rayan has 6

Amelia has 4 boxes of pencils. Each box has

Amelia has 4

6

They have

*p*pencils.*p*+*p*+*p*+*p*+*p*+*p*= 6 ×*p*= 6*p*Rayan has 6

*p*pencils.Amelia has 4 boxes of pencils. Each box has

*p*pencils.*p*+*p*+*p*+*p*= 4 ×*p*= 4*p*Amelia has 4

*p*pencils.6

*p*+ 4*p*= 10*p*They have

**10**pencils altogether.*p*
b) 6

Rayan has

*p*− 4*p*= 2*p*Rayan has

**2**more pencils than Amelia.*p*
c) 2

Rayan has

*p*= 2 ×*p*= 2 × 6 = 12Rayan has

**12**more pencils than Amelia.
The value of

*p*= 6#### 2. Simplify the following expressions.

**a) 5**

*m*+*m*= ?
Let

5

*m*be the number of marbles in each bag.5

*m*+*m*= 6*m***b) 5**

*m*− 2*m*= ?5

*m*− 2

*m*= 3

*m*

**c) 5**

*m*− 3*m*+ 2*m*= ?5

*m*− 3

*m*+ 2

*m*= 2

*m*+ 2

*m*= 4

*m*

**d) 5**

*m*+ 6 − 2*m*− 3 = ?
5

*m*+ 6 − 2*m*− 3 = 5*m*− 2*m*+ 6 − 3 = 3*m*+ 3
5

6 − 3 = 3

*m*− 2*m*= 3*m*6 − 3 = 3

#### 3. Find the value of each of the expressions below when *b* = 4.

**a) 5**

*b*− 2*b*+ 2= 3

*b*+ 2 (Simplify)

= (3 ×

*b*) + 2

= (3 × 4) + 2 (Put the value of

*b*as 4)

= 12 + 2

=

**14**

**b)**

8b + 3 |

5 |

=

(8 x 4) + 3 |

5 |

=

32 + 3 |

5 |

=

35 |

5 |

=

**7**

#### 4. Jane has *t* stamps. Jill has 3 times as many stamps as Jane and Julia has 2 stamps more than Jane.

a) Express the number of stamps that they have altogether in terms of *t*.

b) How many more stamps has Jill than Julia if Jane has 8 stamps?

a) Jane has

*t*stamps.

Jill has 3 ×

*t*stamps or 3

*t*stamps.

Julia has

*t*+ 2 stamps.

Total stamps =

*t*+ 3

*t*+

*t*+ 2 =

**5**

*t*+ 2
b) 3

Jill has 2

Now, replace

2

Jill has

*t*−*t*− 2 = 2*t*− 2Jill has 2

*t*− 2 more stamps than Julia.Now, replace

*t*by 8.2

*t*− 2 = 2 × 8 − 2 = 14Jill has

**14**more stamps than Julia.#### 5. A zoo has 3 times as many terrestrial animals as aquatic animals and 122 more aquatic animals than amphibians.

a) Write an algebraic expression to express the total number of animals in the zoo in terms of the number of aquatic animals.

b) If there are 1633 animals in the zoo altogether, how many terrestrial animals are there?

a) To express the total number of animals in terms of the number of aquatic animals, we assume the number of aquatic animals to be

Number of aquatic animals =

Number of terrestrial animals = 3

Number of amphibians =

Total number of animals =

Total number of animals in the zoo is

*k*.Number of aquatic animals =

*k*Number of terrestrial animals = 3

*k*Number of amphibians =

*k*− 122Total number of animals =

*k*+ 3*k*+*k*− 122 = 5*k*− 122Total number of animals in the zoo is

**5**where*k*− 122*k*is the number of aquatic animals.
b) 5

5

3

There are

*k*− 122 = 16335

*k*= 1633 + 122 = 1755*k*= 1755 ÷ 5 = 3513

*k*= 3 × 351 = 1053There are

**1053**terrestrial animals in the zoo.#### 6. A memory card costs $69. A digital camera costs $16*y* more than the memory card. A tripod stand costs $*y* less than the memory card.

a) If Eric bought all the three items, how much did he pay? Express your answer in terms of *y*.

b) If the tripod stand cost $39, find the cost of the camera.

a) Cost of memory card = $69

Cost of digital camera = $69 + $16

*y*

Cost of tripod stand = $69 − $

*y*

Total cost of all items = $69 + $69 + $16

*y*+ $69 − $

*y*= $207 + $15

*y*

Eric paid

**$207 + $16**for all the three items.

*y*
b) Cost of tripod stand = $69 − $

Cost of camera = $69 + $16

= $69 + ($16 ×

= $69 + ($16 × 30)

= $69 + $480

= $549

The cost of the camera is

*y*= $39*y*= 30Cost of camera = $69 + $16

*y*= $69 + ($16 ×

*y*)= $69 + ($16 × 30)

= $69 + $480

= $549

The cost of the camera is

**$549**.#### 7. A bag of chips has a mass of *q* grams and a box of cookies has twice as much mass.

a) What is the mass of a box of cookies in terms of *q*?

b) Nur bought 3 bags of chips and some boxes of cookies. The total mass of the items she bought was 1.8 kg. What was the mass of cookies that she bought expressed in terms of *q*?

c) If each bag of chips had a mass of 120 grams, how many boxes of cookies did she buy?

a)

The mass of a box of cookies is

The mass of a box of cookies is

**2**grams.*q*
b)

Total mass of items = 1.8 kg = 1800 grams

Mass of 3 bags of chips = 3 ×

Mass of all the boxes of cookies =

Total mass of items = 1.8 kg = 1800 grams

Mass of 3 bags of chips = 3 ×

*q*grams = 3*q*gramsMass of all the boxes of cookies =

**(1800 − 3**grams*q*)
c) Mass of 1 box of cookies = 2

= 2 × 120

= 240 grams

Mass of all the boxes of cookies = (1800 − 3

= (1800 − 3 × 120) grams

= (1800 − 360) grams

= 1440 grams

Total number of boxes of cookies = 1440 ÷ 240 = 6

Nur bought

*q*grams= 2 × 120

= 240 grams

Mass of all the boxes of cookies = (1800 − 3

*q*) grams= (1800 − 3 × 120) grams

= (1800 − 360) grams

= 1440 grams

Total number of boxes of cookies = 1440 ÷ 240 = 6

Nur bought

**6**boxes of cookies.