Matches were used to make the following pattern:
Complete the table for the above pattern:
| \text{Number of triangles } (t) | 1 | 2 | 3 | 5 | 10 | 20 |
|---|---|---|---|---|---|---|
| \text{Number of matches } (m) |
Write a formula that describes the relationship between the number of matches (m) and the number of triangles (t).
How many matches are required to make 25 triangles using this pattern?
Complete the table for the above pattern:
| \text{Number of triangles } (t) | 1 | 2 | 3 | 5 | 10 | 20 |
|---|---|---|---|---|---|---|
| \text{Number of matches } (m) |
Write a formula that describes the relationship between the number of matches (m) and the number of triangles (t).
How many matches are required to make 74 triangles using this pattern?
Consider the pattern for blue boxes below:
Complete the table:
| \text{Number of columns } (c) | 1 | 2 | 3 | 5 | 10 | 20 |
|---|---|---|---|---|---|---|
| \text{Number of blue boxes } (b) |
Write a formula that describes the relationship between the number of blue boxes (b) and the number of columns (c).
State the number of blue boxes, b, required for:
38 columns
92 columns
State the number of columns, c, that would contain:
45 blue boxes
51 blue boxes
James is making snowflakes out of hexagonal tiles:
He creates a table comparing the width of a snowflake to the number of tiles needed to make it:
| \text{Width } \left(W\right) | 1 | 3 | 5 | 7 | 9 | 11 | 13 |
|---|---|---|---|---|---|---|---|
| \text{Number of tiles } \left(T\right) | 1 | 7 | 13 | 19 |
How many new tiles are added at each step?
Find how many tiles James will need to make the next three snowflakes in the sequence by completing the table of values.
Which of the following equations represents the relationship between a snowflake's width and the number of tiles needed?
Hence, find the number of tiles required if the width of the snowflake is 21.
The height of a candle is measured at 15-minute intervals and is shown in the figure:
Complete the table of values below:
| \text{Time (minutes)} | 15 | 30 | 45 | 60 |
|---|---|---|---|---|
| \text{Height (cm)} |
For each table below, write an equation for the dependant variable in terms of the independant variable:
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y | 9 | 10 | 11 | 12 | 13 |
| x | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|
| y | 14 | 15 | 16 | 17 | 18 |
| h | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| k | 5 | 10 | 15 | 20 | 25 |
| p | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|
| q | 1 | 2 | 3 | 4 | 5 |
| p | 0 | 7 | 14 | 21 | 28 |
|---|---|---|---|---|---|
| q | - 9 | - 8 | - 7 | - 6 | - 5 |
| f | 9 | 10 | 11 | 12 | 13 |
|---|---|---|---|---|---|
| g | 4 | 5 | 6 | 7 | 8 |
| f | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|
| g | 8 | 10 | 12 | 14 | 16 |
| f | 7 | 14 | 21 | 28 | 35 |
|---|---|---|---|---|---|
| g | 1 | 2 | 3 | 4 | 5 |
| x | 3 | 8 | 13 | 18 |
|---|---|---|---|---|
| y | 34 | 84 | 134 | 184 |
| r | 24 | 28 | 32 | 36 | 40 |
|---|---|---|---|---|---|
| t | 6 | 7 | 8 | 9 | 10 |
| a | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| b | - 3 | 2 | 7 | 12 | 17 |
| a | 0 | 6 | 12 | 18 | 24 |
|---|---|---|---|---|---|
| b | 8 | 9 | 10 | 11 | 12 |
| a | 0 | \ldots | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|
| b | 9 | \ldots | 30 | 33 | 36 | 39 |
| m | 0 | \ldots | 42 | 48 | 54 | 60 |
|---|---|---|---|---|---|---|
| n | 4 | \ldots | 11 | 12 | 13 | 14 |
The table below shows amounts of money, x, put into a bank, and the corresponding amounts, y, in the bank after a year.
| x | \$400 | \$500 | \$600 | \$700 | \$800 |
|---|---|---|---|---|---|
| y | \$600 | \$750 | \$900 | \$1050 | \$1200 |
Use the table of values to write an equation for y in terms of x.
Write an expression for the perimeter of the rectangle in terms of n.
Write an expression for the perimeter of the triangle in terms of b.
The perimeter of this triangle is 189\text{ cm}.
Write the perimeter of the triangle in terms of x.
Solve for the value of x.
Given that the perimeter of this triangle is 98\text{ cm}, form an equation in terms of x and hence solve for the unknown.
The following quadrilateral has a perimeter of 315\text{ cm}:
Write an expression that represents the perimeter in terms of x.
Solve for the value of x.
Write the statements below as equations and solve them. Let x represent the unknown number:
If 11 is subtracted from a number the result is - 7.
The quotient of a number and - 3 is - 20.
Write the statements below as equations and solve them for x:
The sum of 8 and 12 x is equal to 92.
The product of 5 and the sum of x and 7 equals 50.
Kate and Isabelle do some fundraising for their sporting team. Together they raised \$600. If Kate raised \$272 more than Isabelle, and Isabelle raised \$p:
Write an equation in terms of p that represents the relationship between the different amounts, and then solve for p.
How much did Kate raise?
John and Uther do some fundraising for their sporting team. Together they raised \$403. If John raised \$ m, and Uther raised \$71:
Write an equation that represents the relationship between the amounts each contributed.
Find the value of m.
The cost of a cricket ball is 136 cents more than the cost of a rugby ball.
Let \$x be the cost of a cricket ball and \$y be the cost of a rugby ball.
Express x in terms of y
8 cricket balls and 9 rugby balls cost \$119. Write this statement as an equation in terms of x and y.
Find the value of y.
Find the value of x, the cost of a cricket ball.
Beth is 7 times as old as James. Let x be the present age of Beth in years and y be the present age of James in years.
Express x in terms of y.
In 2 years time, Beth will be 5 times as old as James. Express this sentence as an equation in terms of x and y.
Find the value of y.
Find the value of x, the present age of Beth.
Vanessa is cutting out a rectangular board to construct a bookshelf. The board is to have a perimeter of 48 inches, and its length is to be 3 inches shorter than double the width. Let x be the width of the board.
State the expression for the length of the board in terms of x.
Solve for x, the width of the board.
Hence state the length of the board.
A website advertises properties for sale. If the property is sold within the month, the website charges \$130 for the advertisement, but if the property is not sold within the month, the website pays the advertiser \$20. In a particular month, 58 advertisements were placed, and a total of \$3040 was made across all advertising.
Use an equation to find the number of advertisements that resulted in a sale of the property.
Marge is looking at accommodation prices in Paris. One particular hotel charges \$184.70 for the first night, and then \$153.97 for every additional night. Marge has a budget of \$1108.52.
Use an equation to find how many nights she can afford to stay.