Worksheet 3 – Ratios, Rates, and Proportions

Worksheet 3 – Ra.os, Rates, and Propor.ons MTH1W Jensen Unit 1 – Number Sense 1) Write the ratio of the number of shaded circles to unshaded circles. 4 5 2) Simplify the following ratios no no a) 20:50 12 2 c) 2:22 b) 4:44 1 25 is it d) 21:14 1 11 3 2 3) Complete the following equivalent ratios a) !: 8 = 1: 4 b) !: 8 = 1: 5 c) 9: 9 = !: 32 d) 1.8: 3 = 27: ! x 32 42 8 1 5 9 9 32 32 8 s 45 2 2 8 1 5 18 3 4 27 45 4) For every $100 earned, Jon gets taxed $25. a) Write this scenario as a simplified ratio. 00 25 4 b) If Jon earned $75000 this year how much money did he pay in taxes? 7500 x 7 18750 4Y He paid 18750 intaxes 5) Max and Cal share $84 in the ratio 5:2. How much money does each person get? If the 84 is dividedinto 5 2 7 parts I part Maxgets 5 parts 60 12 5 Cal gets 2 parts 12 84 12 24 2 6) 60 is divided into three parts: A, B, and C, in the ratio 2:5:3. Find the values of A, B, and C. If 60 is dividedinto 2 5 3 10 parts I part 39 6 5 83 3 parts 6 3 18 7) A piece of rope is cut into three lengths in the ratio 6: 7: 10. If the shortest length is 24 m… a) What is the middle length of rope? 4 If the shortest rope is 6 parts I part Middle rope 7 parts 4 7 28m b) What is the longest length of rope? Longest rope 10 parts 4 4 10 40 m c) What is the total length of rope? Total length 24 28 40 92m 8) Write each of the following as the indicated unit rates a) $100 for 5 boxes = $_____ 20 / box b) 24 bottles for $20 = $_____ 1.20/ bottle c) 120 km in 2 hours = _______ 60 km/hour d) $10 for 4 L = $_____ 2.50/ L 9) A box of diapers at Costco contains 174 diapers and costs $40. A box of diapers at Walmart contains 148 diapers and costs $35. Which brand oXers a lower cost per diaper and by how much? Costco Walmart 40 35 0.23perdiaper 174diapers 148diapers 0.24perdiaper Costco is about 0.01cheaperperdiaper 10) 3.1 kg of apples cost $7.13. How much would 2 kg cost? cost perkg 2.30perkg cost of 2kg 2 2.3 4.60 11) 4.2 kg of pears cost $8. How many kg of pears can you buy with $6? Kg perdollar kgwith 6 4.249 8 6 0.525 0.525kgperdollar 3.15 kg 12) Write the following percentages as decimals b) 45% a) 23% 0 180 0.23 0.45 c) 3% d) 128% 128 100 0.03 1.28 13) Write the following as a percentage a) 0.05 ! b) 0.62 09 0,05 # d) 3 $ c) " 1,98 s To 38 5 62 3 3,48 340 25 14) Complete the table Fraction Decimal 7 20 0.35 35 0.08 8 1800 1 Percentage 110% 1.1 15) Rory is considering buying a new pair of Bauer Vapor Hyperlite 2 hockey skates for $1200. Determine the cost of the skates after a 13% sales tax is applied. Tax 1200 13 Total cost 1200 1200 0.13 156 1356 156 16) A computer has a regular price of $910 is on sale for 20% oX. a) Determine the price of the computer after the discount is applied (excluding tax). Discount 910 20 0 Total cost 910 182 910 0.2 ORjustdo 0.8 910 182 728 728 b) Determine the cost of the discounted computer after tax (13% HST) Tax 728 1340 728 0.13 94064 Total cost 728 94.64 822.64 or just do 728 1.13 822.64 c) Does it make a diXerence if the tax is applied before or after taking the discount? Explain. NoThe same multiplications wouldbedone Cost 0.8 910 1.13 910 1.13 008 822.64 The order of the multiplications don'tchangethevalue 17) Percentage increase is the diXerence between a final value and an initial value, expressed as a percentage of the initial value. For example, from 10 to 15 is a 50% increase, since the value increased by 5, which is 50% of 10. Find the percentage increase for the following… a) The price of a shirt increased from $19.99 to $23.99 Difference 23.99 19.99 4 increase Y.gg 20 increase 0.2 20 b) The price of a house increased from $350000 to $600000 Difference 600000 increase 350000 250000 350000 About a 71.43 increase 250000 0.7143 71043 18) Carey’s gross income is $70000/year. After deductions, Carey’s net income is $52000/year. a) What percentage of his gross income is his take-home income? 52000 70000 07429 74.29 b) The 50/30/20 rule is a good budgeting rule that suggests dividing your net income into three categories shown below. Using this guideline, determine how much Carey should allocate to each category. Savings 0.2 52000 10400 Wants 0.3 52000 15600 Needs 0.5 52000 26000 19) A 500 g bag of almonds usually costs $13 and a 200 g bag of almonds costs $9. Today, the 500 g bag is for sale at 10% oX. a) Find the price per gram of the 500 g bag of almonds after the discount in cents. Priceof 500gbags0.9 13 11.7 Pricepergram b) Find the price per gram of the 200g bag of almonds in cents. Pricepergram 2099 0.045pergram c) Which bag of almonds is better value? The 500gbag is a bettervalue g 0.0234pergram