# Simplifying and Evaluating Algebraic Expressions

There areppencils 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 ofp?

Rayan has 6 boxes of pencils. Each box hasppencils.

p+p+p+p+p+p= 6 ×p= 6p

Rayan has 6ppencils.

Amelia has 4 boxes of pencils. Each box hasppencils.

p+p+p+p= 4 ×p= 4p

Amelia has 4ppencils.

6p+ 4p= 10p

They have 10ppencils altogether.

b) How many more pencils has Rayan than Amelia in terms ofp?

6p− 4p= 2p

Rayan has 2pmore pencils than Amelia.

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

The value of p = 62p= 2 ×p

= 2 × 6

= 12

Rayan has 12 more pencils than Amelia.

*Simplify the following expressions.*

*Simplify the following expressions.*

a) 5m+m= ?Letmbe the number of marbles in each bag.

5m+m= 6m

b) 5m− 2m= ?

5m− 2m= 3m

c) 5m− 3m+ 2m= ?

5m− 3m+ 2m= 2m+ 2m

= 4m

c) 5m+ 6 − 2m− 3 = ?

55m− 2m= 3m

6 − 3 = 3m+ 6 − 2m− 3 = 5m− 2m+ 6 − 3

= 3m+ 3

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

*Find the value of each of the expressions below when*

*b*= 4.a) 5b− 2b+ 2

First simplify then put= 34in place of.bb+ 2

= (3 ×b) + 2

= (3 × 4) + 2

= 12 + 2

=14

b)8b+ 3

5= (8 × 4) + 3

5= 32 + 3

5= 35

5= 7

*Word Problem 1*

*Word Problem 1*

Jane haststamps. 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 oft.

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

a) Jane haststamps.

Jill has 3 ×tstamps or 3tstamps.

Julia hast+ 2 stamps.

Total stamps =t+ 3t+t+ 2

= 5t+ 2

b) 3t−t− 2 = 2t− 2

Jill has 2t− 2 stamps more than Julia.

Jane has 8 stamps. Replace2tby 8.t− 2 = 2 × 8 − 2

= 14

Jill has 14 stamps more than Julia.

*Word Problem 2*

*Word Problem 2*

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 k.

Number of aquatic animals = kNumber of terrestrial animals = 3 kNumber of amphibians = k− 122Total number of animals = k+ 3k+k− 122= 5 k− 122

Total number of animals in the zoo is 5k− 122 wherekis the number of aquatic animals.

There are 1053 terrestrial animals in the zoo.

b) 5 k− 122= 1633 5 k= 1633 + 122 = 1755 k= 1755 ÷ 5 = 351 3 k= 3 × 351 = 1053

*Word Problem 3*

*Word Problem 3*

A memory card costs $69. A digital camera costs $16ymore than the memory card. A tripod stand costs $yless than the memory card.

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

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 yCost of tripod stand = $69 − $ yTotal cost of all items = $69 + $69 + $16 y+ $69 − $y= $207 + $15 y

Eric paid $207 + $16yfor all the three items.

b) Cost of tripod stand = $69 − $ y= $39y= 30 Cost of camera = $69 + $16 y= $69 + ($16 × y)= $69 + ($16 × 30) = $69 + $480 = $549

The cost of the camera is $549.

*Word Problem 4*

*Word Problem 4*

A bag of chips has a mass ofqgrams and a box of cookies has twice as much mass.

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

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 ofq?

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 2qgrams.

b)

Total mass of items = 1.8 kg = 1800 grams Mass of 3 bags of chips = 3 × qgrams= 3 qgramsMass of all the boxes of cookies = (1800 − 3 q) grams

c) Mass of all the boxes of cookies = (1800 − 3 q) grams= (1800 − 3 × 120) grams = (1800 − 360) grams = 1440 grams Mass of 1 box of cookies = 2 qgrams= 240 grams Total number of boxes of cookies = 1440 ÷ 240 grams = 6

Nur bought 6 boxes of cookies.