DHS Equations & Inequalities (9758) Topical Revision

2. Equations and Inequalities 1 2. Equations and Inequalities (I) Equations 1 SRJC/2015Prelim/I/1 A landscape gardener is tasked to design a garden with a total area of 140 m2. Part of the garden will be decking, part will be flowers and the rest will be grass. Let the area of decking, the area of flowers and the area of grass, be denoted by d, f and g respectively, all measured in m2. It is required that the area of grass is 20 m 2 more than the total area of flowers and decking. Including labour, each square metre of grass, decking and flowers costs $10, $21 and $42 respectively. The landscape gardener has been instructed to come up with a design that will cost $2900. Find the values of d, f and g that the landscape gardener should use. [4] 2 YJC/2015Prelim/I/1 A confectionery bakes 3 types of cupcakes; blueberry, strawberry and chocolate. Each type is prepared in trays of 12. The time taken to prepare a tray of cupcakes, the mass of flour used for each tray and the selling price of each cupcake are given in the following table. Type of cupcake Preparation Time (min) for each tray Mass of flour (g) for each tray Selling price of a cupcake Blueberry 8 600 $1.00 Strawberry 7 600 $0.90 Chocolate 6 800 $0.80 On a particular day, 17 hours of preparation time was spent and 96 kg of flour was used to make the cupcakes. All the cupcakes were sold and the total amount collected was $1572. By forming a system of linear equations, determine the number of trays of each type of cupcakes made on that day. [4]

2. Equations and Inequalities 2 3 VJC/2009Prelim/I/2 Mr Spongebob went to the supermarket on 3 separate occasions to buy crabs, lobsters and bamboo clams. He observed that while the price of crabs and bamboo clams remained constant, the price of lobsters consistently increased by 10% compared to the immediate previous visit. The amount of crabs, lobsters and bamboo clams that he bought by weight for each visit as well as the total amount spent is shown in the table below. 1st visit 2nd visit 3rd visit Crab (kg) 3.20 5.60 4.50 Lobster (kg) 1.50 1.20 2 Bamboo Clam (kg) 7 6.50 6.50 Total amount paid in $ 277.50 347.00 395.18 What is the price per kilogram for crab, lobster and bamboo clam during Mr Spongebob’s third visit to the supermarket? [5] 4 JJC/2009Prelim/I/6(a) On a farm there a re 3 different types of animals : chickens, horses, and sheep. The farmer confirms that the number of sheep is twice the number of chickens. He also counted a total of 1250 animal legs. Due to his handwriting, he was not sure if there were 250 animals or 350 animals in total. Find the correct number of chickens, horses and sheep. [4] 5 CJC/2015Prelim/II/1 A Singaporean tourist is visiting three countries, Denmark, England and Russia and plans to prepare souvenir packs for her loved ones consisting of 1kg cheese, 1kg chocolate and 1kg candy, wh