Write the following statements as equations:
The length, L, of a box is nine times the width, W.
The weight of a human, H, is seven times the weight of a greyhound, G.
The revenue, R, of a company is double the cost, C.
The length, L, of a swimming pool is triple the width, W.
Write the following statements as equations, where x represents the number:
If 11 is subtracted from a number, the result is - 7.
The quotient of 15 and an unknown number, is 3.
The product of 3, and a number increased by 4, is 27.
Two times a number is equal to 12 decreased by the number.
For each of the following statements:
Write the statement as an equation in which x represents the number.
The sum of a number and 7 is 17.
Seven more than twice a number is 23.
Fifteen minus three-quarters of a number is 9.
Seven times a number is equal to 10 more than twice the number.
The quotient of a number and - 3 is - 20.
Write the statements below as equations and then solve them to find 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.
The difference of 5 from x muliplied by 3 is equal to - 15.
One quarter of a number is equal to triple that number less 22.
Write this word problem as an equation in terms of x.
Solve the equation for x.
Let x be the smallest of three consecutive even integers.
Write an expression for:
The second integer
The third integer
Write an expression for the sum of the first and third consecutive even integers.
Find three consecutive even integers whose sum is 36.
Find four consecutive odd integers whose sum is 64.
Three consecutive integers are such that the sum of the first and twice the second, is 12 more than twice the third. Let x be the smallest of the numbers.
Form an equation and solve it for x.
Find the three consecutive integers.
The perimeter of a square with side length d \text{ cm} is 40 \text{ cm}.
Write an equation in terms of the side length d.
Hence determine d.
The perimeter of the trapezoid below is 27 \text{ cm}.
Write an equation in terms of x and y for the perimeter.
Find the value of y, if x is 5 \text{ cm}.
The perimeter of the following triangle is 189\text{ cm}:
Write an equation 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.
Consider the following quadrilateral with a perimeter of 315\text{ cm}:
Write an expression for the perimeter in terms of x.
Find the value of x.
Consider the angles marked in the following diagram:
Find x, correct to two decimal places.
Find the size of the smaller angle correct to two decimal places.
Consider the two angles given in the diagram:
Calculate the size of one of the angles.
Consider the following triangle:
Find the value of x.
Hence calculate the size of the smallest angle in the triangle.
John and Uther do some fundraising for their sporting team. John raised \$m, and Uther raised \$71. Together they raised \$403. Find the value of m.
Kate and Isabelle do some fundraising for their sporting team. Together they raised \$600. Isabelle raised \$p and Kate raised \$272 more than Isabelle.
Write an equation in terms of p that represents the relationship between the different amounts and solve for p.
Calculate how much money Kate raised.
Vanessa is cutting out a rectangular board to construct a bookshelf. The board is to have a perimeter of 48 \text{ cm} and its length is to be 3 \text{ cm} shorter than double the width. Let x be the width of the board.
Write an expression for the length of the board in terms of x.
Find x, the width of the board.
Hence, find the length of the board.
Sophia is the youngest child in her family. She has three older brothers of ages 19, 16 and 12, and a sister who is eight years older than Sophia. The average age of the five children is 15 years. If Sophia is k years old, find the value of k.
Valentina tries to guess how many people are at a concert, but she guesses 400 too many. Kenneth guesses 150 too few. The average of their guesses is 3625.
Let x be the exact number of people at the concert. Find the value of x.
At present, Patricia's father is 56 years older than Patricia. 3 years ago, her father was 5 times as old as her. Let y represent Patricia's current age. Form an equation and hence find the value of y.
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.
Let n represent the number of nights Marge can stay at the hotel. Write an equation in terms of n and solve it to determine how many nights she can afford to stay.
When a number is added to both the numerator and denominator of \dfrac{1}{5}, the result is \dfrac{3}{7}.
If n represents the number, find the value of n.
Sharon, a tennis player has won 54 out of 78 matches in her career. Let x represent the number of matches she must win in a row to raise her win percentage to 75\%. Find x.
To manufacture sofas, the manufacturer has a fixed cost of \$27\,600 plus a variable cost of \$170 per sofa. Find the number of sofas that need to be produced so that the average cost per sofa is \$290.
To save water, a household decides to install one large and one smaller water tank. The smaller tank will hold 160 litres less than the larger tank, and when the larger tank is \dfrac{3}{5} full, it will be able to completely fill the smaller tank. Let m represent the capacity of the smaller tank. Write an equation and solve it for m.
A commercial airplane has a total mass at take off of 51\ 000 \text{ kg}. The luggage and fuel are \dfrac{1}{3} the mass of the unloaded plane, and the crew and passengers are \dfrac{1}{4} the mass of the fuel and luggage. Let p represent the mass of the unloaded plane. Write an equation and solve it for p.
Edward and Roald both leave Sydney at the same time to go on holidays. Edward travels by car and drives at an average speed of 80 \text{ km/h}. Roald is going 3080 \text{ km} further than Edward, so he travels on a plane which moves at an average speed of 850 \text{ km/h}.
If they each take t hours for their journey, first write an equation in terms of t and then solve it to find out how long they each travelled for.