Express Workshop Units 1-6 Problems. Unit 1 Algebra 1-1. Solve for the unknown: a) 4p 23 9p 7 b) 3( x 8) 5( x 3) 247 c) 12 9

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1 Express Workshop Units 1-6 Problems Unit 1 Algebra 1-1. Solve for the unknown: y11 y8 a) 4p23 9p7 b) 3( x8) 5( x3) 247 c) x y1 5x7y25 y x11 d) e) f) 5x10y 10 11x6y 8 y 2x19 1-2a) The formula for converting temperature from degrees Celsius to degrees 9 Fahrenheit is F C 32. Find the temperature in degrees Celsius when it is Fahrenheit (F). 1-2b) Find the temperature that is the same in degrees Fahrenheit and degrees Celsuius Ryerson s Fashion Design School is selling tickets to their spring fashion show. One the first day of ticket sales, Ryerson sold 7 student tickets and 13 nonstudent tickets for a total of $205. On the second day, Ryerson sold 14 student tickets and 31 non-student tickets for $470. Determine the price per student ticket and the price per non-student ticket A business employs 300 people. It pays $425 per week for skilled workers and $275 per week for unskilled workers. The total bill for the week is $ Find the number of skilled workers.

2 Unit 2 Linear Coordinate Geometry, Linear Systems of Equations and Applications 2-1 Shown below is a chart representing the number of clients using a math tutoring centre, x, and the total expenses for running the centre, y. (Assume a linear relationship exists. Number of Clients Total Expenses x y 0 40 $ $1350 $3975 a) Determine the equation relating the total expenses to the number of clients given in the form y=mx +b. b) State the slope of the line and explain what it represents in words? c) Find the missing values in the chart. d) What is the y-intercept and what does it mean in words? e) If a new model, y37.5x 200 is to better describe the relationship between the number of clients and the total expenses of running a tutoring company, determine the number of clients such that the total expenses of operating a tutoring business will be the same for both models. 2-2 A cell phone company offers two plans. Plan A has a fixed cost of $40 per month and an additional $0.20 per minute of usage. Plan B has a fixed cost of $28 per month but charges $0.32 per minute of usage. For what number of minutes of airtime will the total monthly cost of Plan A and Plan B be equal. 2-3 A cell phone company offers two plans. Plan A has a fixed cost of $45 per month and an additional $0.25 per minutes of usage. Plan B charges $0.55 cents per minutes of usage with no fixed cost. At the end of a particular month, I found that I could have saved exactly $20 had I subscribed to Plan B as compare to Plan A. Determine my minutes of usage that month. (Round to the nearest minute.)

3 Unit 3 Percent Type 1: Regular Percent Questions. (Concept of Part( is) Decimal ) Whole ( of ) 3-1 What percent of 126 is 22? (Round percent to two decimal places.) % of what number is 89.3? (Round answer to two decimal places.) % of 41 is what number? (Round answer to two decimal places.) Type 2: Percent Increase or Decrease Questions 3-4 Grace works as an intern in a bank for $15 per hour. If her pay is increased to $17 per hour, what is her percent increase in pay? 3-5 Find the asking price of a two bedroom condo that eventually sold for $ after it had been reduced by 15%. 3-6 An investment made together by Jared and Nina increased in value to $ by the end of one year. This represented a gain of 18% on the original investment. a) Find the amount they invested together at the beginning of the year. b) If Jared invested $800 more than Nina, how much did each invest? Type 1 or Type 2 Question? 3-7 Year People actually voted in Ward 9 of City of Toronto The chart above represents the number of voters that voted in Ward 9 of the City of Toronto. a) Find the percentage increase from 2000 to 2001, rounded to two decimal places. b) If the number of voters in Ward 9 increased by 12% from 1999 to 2000, find the number of voters in c) If the number of voters in 2002 is 107% of the number of voters in 2001, find the number of voters in Round to the nearest person.

4 Unit 4 Ratio Type 1: Comparing Ratios 4-1. If a:b= 5:32 and it is known that a=46, find the value of b The ratio of people watching the shopping channel to making the purchase on a particular day is 7:3. If a total of 7590 purchases were made on the shopping channel, determine the number of viewers on that particularly day A cruise called Ultimate Comfort charges two different rates for seats. Currently, the ratio of the number of tickets sold at the higher rate compared to the number of tickets sold at the lower rate is 3:11. However, once the recession began, 2000 fewer tickets were sold at the higher rate and 1200 more tickets were sold at the lower rate. As a result, the ratio during the recession was 1:5. Find the number of each type of ticket sold originally. Type 2: Given Total or Difference 4-4. Vicki and Ryan decided to buy a lottery ticket together. Vicki to Ryan s contribution to the ticket is in the ratio of 7:5 respectively. If they won $ , how much would each person receive? 4-5. A method for determining the value of a company is the ratio of the company s assets to its debts. In a company called Xcel, the assets to debts ratio was 21:8. It is also known that the difference between the company s assets and its debts was $ Find the value of the debts of Xcel. More complicated type 2 question Gold and Silver are mixed together in the ratio of 2:3 to produce rings. If the price of gold for the ring is $31.68 per gram and the price of the silver in the ring is $5.80 per gram, determine the amount of gold present in a ring that costs $540. (Round your answer to two decimal places.)

5 Unit 5-Financial Math 5-1. A sum of $3 200 is invested in a bank account where interest is calculated at 6% per annum. a. If this sum is invested for 12 years, what amount will it come to at the end of this twelve year period if interest is calculated as: i. Simple interest ii. Compound interest? iii. Compounded monthly b. What length of time will it take for this sum to amount to $8 000 if interest is calculated as compound interest? Round to two decimal places An investment of $ was made 10 years ago at a fixed annual rate of interest on a bond. Its maturity value was $ Find the fixed rate of annual compound interest on the bond How much do I need to invest today, at 8% per year, compounded daily in a savings account in order to have $ at the end of 16 years for my first car? 5-4. An asset is known to appreciate in value by 12% (simple interest) per year. It was purchased on April, If it was worth $ at the end of 2012, how much was it worth when it was purchased? (note: there are 91 days have passed from Jan 1 to Mar 31.) 5-5 A car is purchased on Sept.1 st for $ For the final 4 months of the year, for tax purposes, it is assumed to depreciate at 4% per month, using a simple interest calculation. Determine amount of depreciation during the final four months of the year.

6 Unit 6 Probability 6-1. A row of inflated balloons sit in a row along a wall. Twelve are red, nine are yellow and four are blue. A person is blind-folded and throws darts at the balloons. a) If only one balloon is hit, determine the probability that the dart hits a blue balloon. b) If two balloons are pierced consecutively, determine the probability that both balloons pierced are red. c) If two balloons are pierced by darts, determine the probability that the pierced balloons are of different colours and the second balloon is yellow. d) If each red balloon is worth $20, each yellow balloon is worth $15 and each blue balloon is worth $10, find the probability of hitting two balloons with a combine total of $ A study has been done to determine whether or not a certain drug leads to an improvement in symptoms for patients with a particular medical condition. The results are as follows 30% of the people in the study shows an improvement. A third of those who showed an improvement did not take the drug. 35% of people in the study did not take the drug. a) Use the information shown above to complete the chart below: All in % Drug No Drug Total Improvement No Improvement Total b) Determine the probability that a person took the drug, given that he/she did not show an improvement c) Determine the probability that a person showed improvement, given that he/she took the drug.

7 Solutions: Unit 1: Algebra 1a) p 6 1b) x 119 c) y 65 1d), 0,1 xy 1e) xy, 2, 5 1f) xy, 10, 1 2a) C 25 degree Celsius 2b) F = C at -40 degree Celsuius 3) $7 per student ticket and $12 per non-student ticket 4) Number of Skilled Workers = 252 Unit 2: Equation of Lines 1a) y17.5x 300 1b) There is increase of $17.50 in expense per client 1c) If x = 0, then y = 300 If y = 3975, x = 210 1d) y-intercept = 300; Fixed expenses is $300 1e) 5 clients 2) 100 minutes 3) approximately 83 minutes Unit 3: Percents & Percent Increase/Decrease 1) 17.46% 2) ) ) 13.3 % increase 5) a) $ b) Nina = $ ; Jared = $ a) 10.76% increase 7b) $ c) $

8 Unit 4: Ratios 1) b = ) people 3) expensive tickets and less expensive tickets 4) Vicki - $ ; Ryan - $ ) Debt - $ ) grams of Gold Unit 5: Financial Math 1a) i) $ ii) $ iii) $ b) years 2) 5.40% 3) P = $ ) P = $ ) I = $ Unit 6: Probability 1a) b) c) d) a) All in % Improvement No Improvement Total Drug No Drug Total b) c)