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9.09 Solving problems with equations

Worksheet
Words to equations
1

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 } 14.

h

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

2

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.

3

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.

4

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.

5

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.

Tables
6

Consider the word statement "y is equal to the product of 7 and x".

a

Write an equation in the form y = \ldots that describes the word statement.

b

Hence, complete the table.

x12345
y
7

Consider the word statement "v is equal to the product of -8 and u".

a

Write an equation in the form v = \ldots that describes the word statement.

b

Hence, complete the table.

u12345
v
8

Consider the word statement "q is equal to p less than 12".

a

Write an equation in the form q = \ldots that describes the word statement.

b

Hence, complete the table.

p-2-1012
q
9

Consider the word statement "19 subtracted from r is equal to s".

a

Write an equation in the form s = \ldots that describes the word statement.

b

Hence, complete the table.

r-2-1012
s
10

Consider the word statement "y is equal to the product of 3 and the sum of x and 4".

a

Write an equation in the form y = \ldots that describes the word statement.

b

Hence, complete the table.

x123510
y
11

Consider the word statement "v is equal to the product of 5 and the sum of u and 2".

a

Write an equation in the form v = \ldots that describes the word statement.

b

Hence, complete the table.

u123510
v
Formulas
12

The area of a rhombus is given by the formula A = \dfrac{1}{2} x y, where x and y are the lengths of the diagonals:

a

Find the area of a rhombus which has short and long diagonal lengths of 4\text{ cm and } 6 \text{ cm} respectively.

b

A particular rhombus has a short diagonal length x = 6 \text{ m} and area \\ A = 33 \text{ m}^2. Find the value of y.

13

The area of a rectangle is given by the formula A = length \times width:

a

If the length of a rectangle is 9 \text{ m} and its width is 3 \text{ m}, find its area.

b

The area of a particular rectangle is 45 \text{ m}^2. If its length is 9 \text{ m}, determine the width of the rectangle.

14

The area of a triangle is given by the formula A = \dfrac{1}{2} \times base \times height:

a

If the base of a triangle is 8 \text{ mm} and its height is 6 \text{ mm}, find its area.

b

A triangle with a height of 4\text{ mm} has an area of 16 \text{ mm}^2. Find the length of the base of the triangle.

15

The perimeter of a triangle with sides of lengths p, q and r is given by the formula \\ P = p + q + r:

a

Find P if the length of each of its three sides are p = 9 \text{ mm}, q = 7 \text{ mm} and \\ r = 5 \text{ mm}.

b

If P =40\text{ mm} and the length of each of the two sides are p= 10 \text{ mm} and \\ q= 12\text{ mm}, what is the length of the third side r?

16

The perimeter of a square with side lengths of s is given by the formula P = 4 \times s:

a

Find P if the length of each side is 3 \text{ m}.

b

Find s if the perimeter is P= 40\text{m}

17

The volume of a rectangular prism is given by the formula V = l \times w \times h, where l , w and h are the dimensions of the prism:

a

Given that a rectangular prism has a length of 9 \text{ m}, a width of 4 \text{ m} and a height of 7 \text{ m}, find its volume.

b

The volume of a particular rectangular prism is 140\text{ cm}^3. If it has a length of 10 \text{ cm} and a width of 7\text{ cm}, find the height, h.

18

The perimeter of a triangle can be calculated with the formula P = a + b + c, where a, b and c are the three side lengths of the triangle. If a triangle has a perimeter of P = 37 \text{ cm} and side lengths a = 14 \text{ cm} and b = 13 \text{ cm}, find the length of the side c.

19

The perimeter of a rectangle is given by the formula P = 2 \times \left(l + w\right) , where l is the length and w is the width:

a

Find the perimeter of the rectangle which has a length of l= 6 \text{ cm} and width of w = 5 \text{ cm}.

b

If a certain rectangle has length l = 7 \text{ cm} and perimeter P = 24 \text{ cm}, find the width w.

20

The speed of a plane can be calculated using the formula S = \dfrac{D}{T}, where D is the distance travelled, T is the time taken and S is the speed.

a

If a plane travels 3600 kilometres in 6 hours, find its speed.

b

If the speed of the plane is 700\, {\text{km/hr}}, find the distance travelled after 4 hours.

21

The formula to convert temperature from Celsius to Fahrenheit is F = 32 + \dfrac{9 C}{5}.

a

If C = 35, find the value of F.

b

If F = 212, find the value of C.

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uses algebraic techniques to solve simple linear and quadratic equations

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