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Translating Words Into Symbols Part A: Translate each of the following expression with a mathematical symbol. + + _____ + _____ _____ _____ × ÷ _____ = _____ 1. Altogether _____ 5. Decrease _____ 2. Sum 6. Product 3. Increase 4. Difference 7. Quotient 8. Is Part B: For the following statements, define two variables and write a linear equation that models the sentence. 1. The sum of two numbers is 7. x_________ +y=7 2. The sum of the width and length of a rectangle is 36 m. l +_________ w = 36 3. The total value of nickels and dimes is 75 cents. 5n + 10d = 75 _________ 4. The cost of the rental is $50 plus $5/h. C___________ = 5h + 50 5. A rectangle is 2 m longer than it is wide. ___________ L=w +2 6. When 3 times the first number is subtracted from the second number, the result is 20. s___________ – 3f = 20 7. Mary has x $5 bills and y $10 bills. a) The total value of bills in dollars. T = 5x + 10y _______________ b) The total number of bills. N=x+y _______________ 8. Aaron has x dimes and y quarters. a) The value of dimes in cents. _________ 10x 0.25y b) The value of quarters in dollars. _________ c) The total value of coins in cents. T = 10x + 25y __________________ d) The total number of coins. N=x+y __________________ Modelling with Linear Equations Model each situation using a linear system. Define two variables and write the equations. 1. Anne deposited $1200 in her bank accounts. How much did she put into her savings account, which pays 9% per year in interest, and her chequing account, which pays 4% per year, if she earned $88 in interest after one year? Let x rep. the amount ($) in Anne’s chequing account y rep. the amount ($) in Anne’s savings account x + y = 1200 0.04x + 0.09y = 88 2. Art’s Car Rental charges $45 to rent a compact car for the day plus an additional $0.18/km. Budget Rentals charges $55/day and $0.10/km. How many kilometres would result in the same charge from both companies? Let d rep. the distance travelled (km) in one day C rep. the amount ($) charged each day Art’s Car Rental: C = 0.18d + 45 Budget Rentals: C = 0.10d + 55 3. Sara has started her own home business selling perfume on-line. Her start-up costs were $2550 for a new computer. She buys the perfume from her supplier for $15 per bottle and sells it for $25 per bottle. Determine the number of bottles she must sell to break even. Let p rep. the number of perfume bottles M rep. the amount of money Expenses: M = 15p + 2550 Revenue: M = 25p 4. Frank has $20 to purchase nickels and dimes from the bank for change for a craft fair. The bank teller gives Frank 300 coins in total. How many nickels and dimes were there? Let d rep. the number of dimes n rep. the number of nickels 0.1d + 0.05n = 20 d + n = 300 5. Milk and cream contain different percents of butterfat. How much 3% milk needs to be mixed with how much 15% cream to give 20 L of 6% cream. Let m rep. the amount (L) of 3% milk c rep. the amount (L) of 15% cream m + c = 20 0.03m + 0.15c = 0.06(20) 0.03m + 0.15c = 1.2 Speed/Distance/Time Relationship distance speed time distance speed time distance time speed d s t 6. Jose travelled the 95 km from Oakville to Oshawa by car and GO train. The car averaged 60 km/h, and the train averaged 90 km/h. The whole trip took 1.5 h. How long was he in the car? Let c rep. the time (hr) travelled by car t rep. the time (hr) travelled by train By Car By Train c + t = 1.5 Speed 60 Time c 90 t 1.5 Total Distanc e 60c 90t 95 60c + 90t = 95 7. A canoeist took 2 hours to travel 12 km down a river. The return trip against the current took 3 hours. What was the average paddling rate of the canoeist? What was the speed of the current? Let c rep. the speed (km/h) of the canoeist r rep. the speed (km/h) of the river Recall: (speed)(time) = distance (c + r)(2) = ______ ___ 12 2 2 c+r=6 (c – r)(3) = ______ ___ 12 3 3 c–r=4