6.02 Solving problems with equations
For each of the following word statements:
Write the word statement as an equation, where p is the unknown number.
Solve the equation.
The sum of an unknown number and 39 is 83.
75 is equal to the sum of an unknown number and 42.
The product of 3 and an unknown number is 18.
-7 multiplied by an unknown number is 84.
17 less than an unknown number is 25.
The quotient of an unknown number and 8 is -12.
2 times the sum of an unknown number and 5\, \text{ is } 14.
The sum of a number and 2 divided by 3 is 6.
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.
Write down the equation that represents the relationship between the total number of lollies and the number of lollies each child receives.
Hence, solve the equation.
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.
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.
Hence, solve the equation.
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.
Write down the equation that represents the relationship between the initial number of marbles and the number of marbles left in her collection.
Hence, solve the equation.
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.
Write down the equation that represents the relationship between the total cost and the individual costs of the hat and dress.
Hence, find the cost of the hat if the cost of the dress is \$56.
Consider the word statement "y is equal to the product of 7 and x".
Write an equation in the form y = \ldots that describes the word statement.
Hence, complete the table.
| x | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| y |
Consider the word statement "v is equal to the product of -8 and u".
Write an equation in the form v = \ldots that describes the word statement.
Hence, complete the table.
| u | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| v |
Consider the word statement "q is equal to p less than 12".
Write an equation in the form q = \ldots that describes the word statement.
Hence, complete the table.
| p | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| q |
Consider the word statement "19 subtracted from r is equal to s".
Write an equation in the form s = \ldots that describes the word statement.
Hence, complete the table.
| r | -2 | -1 | 0 | 1 | 2 |
|---|---|---|---|---|---|
| s |
Consider the word statement "y is equal to the product of 3 and the sum of x and 4".
Write an equation in the form y = \ldots that describes the word statement.
Hence, complete the table.
| x | 1 | 2 | 3 | 5 | 10 |
|---|---|---|---|---|---|
| y |
Consider the word statement "v is equal to the product of 5 and the sum of u and 2".
Write an equation in the form v = \ldots that describes the word statement.
Hence, complete the table.
| u | 1 | 2 | 3 | 5 | 10 |
|---|---|---|---|---|---|
| v |
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:
Find the area of a rhombus which has short and long diagonal lengths of 4\text{ cm and } 6 \text{ cm} respectively.
A particular rhombus has a short diagonal length x = 6 \text{ m} and area \\ A = 33 \text{ m}^2. Find the value of y.
The area of a rectangle is given by the formula A = length \times width:
If the length of a rectangle is 9 \text{ m} and its width is 3 \text{ m}, find its area.
The area of a particular rectangle is 45 \text{ m}^2. If its length is 9 \text{ m}, determine the width of the rectangle.
The area of a triangle is given by the formula A = \dfrac{1}{2} \times base \times height:
If the base of a triangle is 8 \text{ mm} and its height is 6 \text{ mm}, find its area.
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.
The perimeter of a triangle with sides of lengths p, q and r is given by the formula \\ P = p + q + r:
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}.
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?
The perimeter of a square with side lengths of s is given by the formula P = 4 \times s:
Find P if the length of each side is 3 \text{ m}.
Find s if the perimeter is P= 40\text{m}
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:
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.
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.
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.
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:
Find the perimeter of the rectangle which has a length of l= 6 \text{ cm} and width of w = 5 \text{ cm}.
If a certain rectangle has length l = 7 \text{ cm} and perimeter P = 24 \text{ cm}, find the width w.
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.
If a plane travels 3600 kilometres in 6 hours, find its speed.
If the speed of the plane is 700\, {\text{km/hr}}, find the distance travelled after 4 hours.
The formula to convert temperature from Celsius to Fahrenheit is F = 32 + \dfrac{9 C}{5}.
If C = 35, find the value of F.
If F = 212, find the value of C.