Zara thinks of a number. She doubles it and then adds 7. Her answer is 31.
Form an equation and solve it to find Zara's number. You must show your working.
(3 marks)C34 · Both tiers · A21
Forming equations from situations
Priya, Tom and Ava share some stickers.
Tom has 5 more stickers than Priya. Ava has twice as many stickers as Tom. Altogether they have 83 stickers.
(a)
Priya has stickers. Show that .
(3 marks)(b)
Work out how many stickers Ava has.
(2 marks)(c)
Ava says she has more than half of all the stickers. Is Ava correct? You must show how you get your answer.
(2 marks)At a cinema, an adult ticket costs £ and a child ticket costs £4 less than an adult ticket. Two adults and three children pay £58 altogether.
(a)
Work out the cost of an adult ticket.
(3 marks)(b)
A family of one adult and four children has £45. Do they have enough money? You must show how you get your answer.
(2 marks)A theatre sells adult tickets for £12 and child tickets for £7. A group buys 9 tickets for £88. How many adult tickets does the group buy?
(3 marks)A rectangle has length cm and width cm. A square has sides of length cm. The rectangle and the square have the same perimeter.
Which shape has the greater area, and by how much? You must show your working.
(4 marks)A rectangular garden is 24 m long and 18 m wide. A path of uniform width is made inside all four edges. The remaining central rectangle has area 280 Work out the width of the path.
(3 marks)A tank contains 12 litres of a mixture that is 20% concentrate by volume. A second mixture is 45% concentrate. How many litres of the second mixture must be added to make a mixture that is 30% concentrate? Assume volumes add. You must show your working.
(3 marks)A tank holds 40 litres of a mixture containing 25% concentrate. Some well-mixed liquid is removed and replaced by the same volume of pure concentrate. The tank then contains 40% concentrate. How many litres were removed? You must show your working.
(3 marks)A rider cycles 36 km along a route and returns along the same route. Her return speed is 3 km/h greater than her outward speed. Her total cycling time is 7 hours. Assuming constant speed on each part, find her outward speed.
(3 marks)A small auditorium has 330 seats arranged in rows. Each row has 3 more seats than the row immediately in front. The back row has three times as many seats as the front row. Work out the number of rows. You may use: sum of an arithmetic sequence = number of terms (first term + last term).
(4 marks)