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Published in: Mathematics
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Finding unknown using proportionality

Divya J / Dubai

15 years of teaching experience

Qualification: CAIE and Pearson Examiner for IGCSE an AS Levels, Masters in Mathematics

Teaches: SAT, ACT, Maths, IGCSE/AS/AL, Physics, Biology, Chemistry, Mathematics

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  1. Mathematics Ratio and Proportion Today's Targets O Finding unknown using proportionality Lecture No .- 09
  2. Proportion Calculating quantities that are in proportion: If two quantities are in direct proportion: When one is multiplied or divided by a number, so is the other. Their ratio stays the same as they increase or decrease. If 4 muffins require 100 grams of flour, then 12 muffins require 300 grams of flour (by multiplying both quantities by a scale factor of 3).
  3. Question Arjun and Gretal each pay rent. In 2018, the ratio of the amount each paid in rent was Arjun : Gretal = 5 : 7. In 2019, the ratio ofthe amount each paid in rent was Arjun : Gretal = 9 : 13. Arjun paid the same amount of rent in both 2018 and 2019. Gretal paid $290 more rent in 2019 than she did in 2018. Work out the amount Arjun paid in rent in 2019.
  4. Question Work out which bag of flour is the best value. Show all your working. Bag A 850 g 55 cents Bag B 950 g 60 cents NOT TO SCALE Bag C 1250 g 80 cents
  5. Question A recipe uses 550 gof flour to make 8 cakes. Work out the amount of flour needed to make 360 cakes. Give your answer in kilograms.
  6. Question $.35 per hour 848 per hour Fixed charge $40 For the first 2 hours plus then $26.50 per hour $.32 per hour These are the rates charged by a painter, a plumber and an electrician who do some work for Mr Sharma. (a) The painter works for 7 hours. Calculate the amount Mr Sharma pays the painter. (b) Mr Sharma pays the plumber $252. Calculate how many hours the plumber works.
  7. Question $.35 per hour 848 per hour Fixed charge $40 For the first 2 hours plus then $26.50 per hour $.32 per hour These are the rates charged by a painter, a plumber and an electrician who do some work for Mr Sharma. (c) Mr Sharma pays the electrician $224. Calculate how many hours the electrician works. (d) Write down the ratio of the amount Mr Sharma pays to the painter, the plumber and the electrician. Give your answer in its lowest terms. Painter : plumber : electrician =
  8. Question A paint mix uses red and white paint in a ratio of 1 : 12. (a) How much white paint will be needed to mix with 1.4 litres of red paint? (b) If a total of 15.5 litres of paint is mixed, calculate the amount of white paint and the amount of red paint used. Give your answers to the nearest 0.1 litre.
  9. Question A recipe uses 150 g butter, 500 g flour, 50 g sugar and 100 g currants to make 18 small cakes. (a) How much of each ingredient will be needed to make 72 cakes? (b) How many whole cakes could be made with 1 kg of butter?
  10. Question Sand and gravel are mixed in the ratio 5: 3 to form ballast. (a) How much gravel is mixed with 750 kg of sand? (b) How much sand is mixed with 750 kg of gravel?
  11. Question Coffee sachets are sold in three different sizes of box. Coffée Sachets 12 E 5.65 Small CoftOc Sachets 35 E15.75 Medium Coffée Sachets 35 €15.75 Large A small box has 12 coffee sachets and costs E5.65. A medium box has 20 coffee sachets and costs E9.20. A large box has 35 coffee sachets and costs E15.75. Work out which size of box gives the best value for money. You must show all your working.
  12. Question Toothpaste is sold in three different sizes of tube. f ootnpø 50 ml A 50 ml tube costs El.09 A 75 ml tube costs El.68 A 125 ml tube costs E2.69 75 ml 125 ml Which tube of toothpaste is the best value for money? You must show all your working.
  13. Question A shop sells bags of crisps in different size packs. There are 18 bags of crisps in a small pack. 20 bags of crisps in a medium pack. 26 bags of crisps in a large pack. Crisps 18 bags E4 each pack CRAB BAG WALKERS Crisps 20 bags E4.99 each pack GRAB BAG WALKERS Crisps 26 bags E6,00 each pack Which size pack is the best value for money? You must show all your working.
  14. Question Blueberries are sold in small cartons and in large cartons. Blueberries 125 g El .60 Small carton Blueberries 225 g €2.80 Large carton There are 125 g of blueberries in a small carton. Each small carton costs El.60 There are 225 g of blueberries in a large carton. Each large carton costs E2.80 Which size of carton is the better value for money? You must show your working.
  15. Question Plants are sold in three different sizes of tray. A small tray of 30 plants costs E6.50 A medium tray of 40 plants costs E8.95 A large tray of 50 plants costs E10.99 Kaz wants to buy the tray of plants that is the best value for money. Which size tray of plants should she buy? You must show all your working.
  16. Question Milk is sold in two sizes of bottle. 4 pints El.18 A 4 pints bottle of milk costs El.18 A 6 pints bottle of milk costs El.74 Milk 6 pints El .74 Which bottle of milk is the best value for money? You must show all your working.
  17. [S16, 42, QId] Q. Mr Chan hires a car in Los Angeles. The charges are shown below. Car Hire. $28.00 per day plus $6.50 per day insurance. $1.25 for every kilometre travelled after the first 800 km. The first 800 km are included in the price. Mr Chan hired the car for 12 days and paid $826.50. (i) Find the number of kilometres Mr Chan travelled in this car. .........„ km [41
  18. [W16, 43, Q] Q. A jigsaw puzzle has edge pieces and inside pieces. The ratio edge pieces : inside pieces = 3 : 22. (i) There are 924 inside pieces. Calculate the total number of pieces in the puzzle. .... ... ......„ [21
  19. [W16, 43, Q] Q. Anjum and Betty spent a total of 9 hours completing the puzzle. The ratio Anjum's time : Betty's time = 7 : 5. .................. hours [2] Work out how much time Anjum spent on the puzzle.
  20. [SIB, 42, Q] (a) Here isa list of ingredients to make 20 biscuits. 260 g of butter 500 g of sugar 650 g of flour 425 gof rice (i) Find the mass of rice as a percentage of the mass of sugar. (ii) Find the mass of butter needed to make 35 of these biscuits. ....„...% [11 [21
  21. [S18, 42, Q] Some people who work for a company are in the following age groups. Group A Under 30 years Group B 30 to 50 years Group C Over 50 years The ratio of the number in group A to the number in group B is 7 : 10. The ratio of the number in group B to the number in group C is 4 : 3. (i) Find the ratio of the number in group A to the number in group C. Give your answer in its simplest form. (ii) There are 45 people in group C. Find the total number of people who work for the company.

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