 # 6.01 Writing expressions and formulae using algebra

Worksheet
Algebraic expressions
1

Using the given key, state how many oranges are represented in the following diagrams using algebra:

a
b
c
d
2

Let m be the number of matchsticks in a full box. Write down an expression to represent the number of matchsticks there are if we have five full boxes and eight loose matchsticks.

3

Write an algebraic expression for each of the following phrases:

a

The sum of u and 11

b

15 less than a

c

n plus one

d

m is increased by two

e

Three times a number n

f

The product of 9 and the variable m

g

7 multiplied by x

h

8 more than 5 x

i

3 less than 8 y

j

Four times y take away 9

k

The product of 9 u and 8

l

The sum of 14 multiplied by v and 20

m

15 times the result of v reduced by 6

n

The quotient of b and 18

o
15 less than the quotient of p and 6
p

The quotient of 8 u and 9

q

8 more than the quotient of 9 and x

r

The difference of a and b, divided by 6

Algebraic equations
4

Write an equation for each of the following sentences:

a

y is equal to six.

b

y is 2 more than x.

c

y is 4 less than x.

d

y is 18 times k.

e

y is 20 times x plus 14.

f

y is 9 times x minus 2.

g

y is x divided by 3 minus 3.

h

y is x divided by 3 plus 12.

i

y equals five times the sum of x and ten.

j

y is the sum of x and 2, divided by 5.

5

Write an equation for each of the following sentences:

a

c is \dfrac{1}{10}th of d.

b

n minus nine equals four.

c

The sum of a and two is equal to three.

d

a is the difference of b and 7, divided by 2.

e

f is 5 less than the quotient of g and 4 .

f

Five times m is equal to double the difference of b and 10.

g

x is equal to 3 groups of the sum of a and b.

h

q is added to p, and the result is one less than triple r.

i

m is equal to 7 groups of the difference between n and 8, then increased by 4.

j

The product of a and b is the same as 11 more than the quotient of a and b.

6

Let the variable q represent the unknown number. Write an equation for the phrase below:

"The sum of one third of a number and eight is equal to four less than the number."

Find unknown values
7
a

Can we solve 2 x + 6?

b

Can we solve 2 x + 6 = 12?

c

8

For each of the following sentences:

i

Write an algebraic equation.

ii

Find the value of n.

a

n plus ten equals eighteen.

b

n minus nine equals ten.

c

n multiplied by five gives you fifteen.

d

n is divided by two to give five.

9

For each of the following word statements:

i

Write the word statement as an equation, where p is the unknown number.

ii

Solve the equation.

a

The sum of an unknown number and 39 is 83.

b

75 is equal to the sum of an unknown number and 42.

c

The product of 3 and an unknown number is 18.

d

-7 multiplied by an unknown number is 84.

e

17 less than an unknown number is 25.

f

The quotient of an unknown number and 8 is -12.

g

2 times the sum of an unknown number and 5\, \text{ is } 8.

h

The sum of a number and 2 divided by 3 is 6.

Applications
10

If y represents the population of a country, write the expression that represents 4.5 times this population.

11

The other day Tina bought k chart-topping albums from Empire Records for \$52. Write an expression for the average cost of each album. 12 Kate, a sandwich maker, produces 10 sandwiches on average per hour. How many sandwiches will she produce in v hours? 13 Yvonne earns \$90 per week delivering newspapers.

a

Write an expression for how much she will earn in u weeks.

b

How much will she earn in 3 weeks?

14

Two angles are supplementary if they sum to 180 \degree. If one angle is y \degree, write an expression for the supplementary angle.

15

The number of students majoring in physics at a particular university is 2200 fewer than the number of students majoring in computer science. If the number of students majoring in computer science is m, write an expression for the number of students are majoring in physics.

16

One foot is equal to 0.305 metres. If Jack's height in metres is a, write an expression for his height in feet.

17

Roxanne has been out picking flowers, and has 40 in total. When she returns, she puts them in 5 different vases. If she puts p flowers in each vase, rewrite the following sentence using algebra:

"There are 5 groups of p flowers, which make 40 in total."

18

Consider the shape in the diagram shown:

If A represents the total area of the shape, rewrite the following sentence as an equation:

"The total area of the shape is equal to the product of a and b, added to the product of b and c".

19

A bag of lollies contains 80 lollies. The lollies are shared evenly between 10 children.

Let n represent the number of lollies each child receives.

a

Write down the equation that represents the relationship between the total number of lollies and the number of lollies each child receives.

b

Hence, solve the equation.

20

Justin divides a deck of cards into 7 even piles. There are 12 cards in each pile.

Let c represent the total number of cards in the deck.

a

Write down the equation that represents the relationship between the total number of cards in the deck and the number of cards in each pile.

b

Hence, solve the equation.

21

Tricia gives Tom 25 marbles from her collection. Tricia now has only 44 marbles in her collection.

Let m represent the number of marbles she had before giving some away.

a

Write down the equation that represents the relationship between the initial number of marbles and the number of marbles left in her collection.

b

Hence, solve the equation.

22

Lisa bought a hat and a dress for a total of \$80. Let h represent the cost of the hat and d represent the cost of the dress. a Write down the equation that represents the relationship between the total cost and the individual costs of the hat and dress. b Hence, find the cost of the hat if the cost of the dress is \$56.