Recipes and floor plans questions with answers

Questions

1. Question 1A recipe for a different number of servings

   The table shows a recipe for chocolate cake for 8 servings. Find the mass, in grams, of cocoa powder needed for 19 servings.

   Ingredient	For 8 servings
   self-raising flour	240 g
   sugar	200 g
   cocoa powder	60 g
   butter	160 g
   eggs	4 eggs

   Show the worked solution

   1. Step 1: Find the amount for 1 serving$\dfrac{60}{8} = 7.5 \text{ g}$
   2. Step 2: Multiply by the number of servings wanted$7.5 \times 19 = 142.5 \text{ g}$142.5 g of cocoa powder is needed.
2. Question 2The most servings you can make (round down)

   The table shows a recipe for prawn fried rice for 3 servings. Nur has 1.85 kg of prawns, 500 g of frozen peas and 450 ml of cooking oil, and plenty of everything else. Find the greatest number of servings Nur can make.

   Ingredient	For 3 servings
   rice	270 g
   prawns	240 g
   frozen peas	90 g
   eggs	3 eggs
   cooking oil	45 ml

   Show the worked solution

   1. Step 1: Each ingredient: what you have ÷ the amount for 1 serving (in g, ml or eggs), then whole servings$\text{prawns: } \dfrac{1850}{80} = 23.125 \rightarrow 23$$\text{frozen peas: } \dfrac{500}{30} = 16.666\ldots \rightarrow 16$$\text{cooking oil: } \dfrac{450}{15} = 30 \rightarrow 30$
   2. Step 2: The ingredient that runs out first decidesThe frozen peas runs out first: at most 16 servings.
3. Question 3Packs to buy and their cost (round up)

   The table shows a recipe for pancakes for 4 servings, and how the ingredients are sold. Chen Wei is making 12 servings and has to buy all the plain flour and eggs. Find the least amount Chen Wei pays for them.

   Ingredient	For 4 servings	Sold in	Price
   plain flour	200 g	1 kg bag	$2.85
   milk	300 ml	1 litre carton	$3.40
   eggs	2 eggs	tray of 10	$3.60
   butter	30 g	250 g block	$4.95
   sugar	25 g	1 kg bag	$2.20

   Show the worked solution

   1. Step 1: Plain flour: the amount needed, then whole packs (pack size in g)$\dfrac{200}{4} \times 12 = 600 \text{ g}$$\dfrac{600}{1000} = 0.6 \rightarrow 1 \text{ packs}$$1 \times 2.85 = 2.85$
   2. Step 2: Eggs: the amount needed, then whole packs (pack size in eggs)$\dfrac{2}{4} \times 12 = 6$$\dfrac{6}{10} = 0.6 \rightarrow 1 \text{ packs}$$1 \times 3.60 = 3.60$
   3. Step 3: Add the two costs (in dollars)$2.85 + 3.60 = 6.45$The least amount is $6.45.
4. Question 4Floor area of an L-shape, and its cost

   The diagram shows the floor plan of an L-shaped living and dining area. The floor is to be covered with vinyl flooring costing $32.50 per m². Find the cost of the flooring.

   Show the worked solution

   1. Step 1: The whole rectangle, then the corner cut out (in m²)$7.5 \times 5.6 = 42$$3.2 \times 1.6 = 5.12$
   2. Step 2: Floor area = rectangle − corner$42 - 5.12 = 36.88 \text{ m}^2$
   3. Step 3: Cost = area × cost per m² (in dollars)$36.88 \times 32.50 = 1198.60$The flooring costs $1,198.60.
5. Question 5Tiles for a floor, bought in boxes

   The diagram shows the floor plan of a flat. The kitchen floor is to be covered with square tiles of side 45 cm. The tiles are sold in boxes of 15, at $48.30 per box. Find the least cost of the tiles for the kitchen.

   Show the worked solution

   1. Step 1: Tiles along each side of the kitchen: change metres to cm, then divide by the tile's side$\dfrac{360}{45} = 8$$\dfrac{180}{45} = 4$
   2. Step 2: Number of tiles$8 \times 4 = 32$
   3. Step 3: Boxes: whole boxes only$\dfrac{32}{15} = 2.133\ldots \rightarrow 3 \text{ boxes}$
   4. Step 4: Cost (in dollars)$3 \times 48.30 = 144.90$The tiles cost $144.90.
6. Question 6Skirting board or paint for a room

   The diagram shows the floor plan of a flat. Skirting board is fixed along the bottom of the bedroom's walls, all the way round except across the doorway, which is 0.8 m wide. Skirting board is sold in 3 m lengths at $9.50 each. Find the least cost of the skirting board.

   Show the worked solution

   1. Step 1: Perimeter of the bedroom (in m)$2 \times (4.2 + 5) = 18.4$
   2. Step 2: Leave out the doorway$18.4 - 0.8 = 17.6 \text{ m}$
   3. Step 3: Lengths of skirting: whole lengths only$\dfrac{17.6}{3} = 5.866\ldots \rightarrow 6 \text{ lengths}$
   4. Step 4: Cost (in dollars)$6 \times 9.50 = 57$The skirting board costs $57.
7. Question 7Real area from a scale plan

   The diagram shows the floor plan of a flat, drawn to a scale of 1 : 40. The lengths marked are measured on the plan. Find the actual floor area of the kitchen, in m².

   Show the worked solution

   1. Step 1: Real lengths from the plan (in cm)$9 \times 40 = 360 \text{ cm}$$6 \times 40 = 240 \text{ cm}$
   2. Step 2: Change to metres (÷ 100)$360 \text{ cm} = 3.6 \text{ m}$$240 \text{ cm} = 2.4 \text{ m}$
   3. Step 3: Real area = length × breadth (in m²)$3.6 \times 2.4 = 8.64 \text{ m}^2$The kitchen's floor area is 8.64 m².