L24 Problem Solving with Equations.notebook March 12, 2015 Review: Solving Equations Substitute, then solve 3x + 2y = 12 a) 456 = 3.14x2 b) 90 = 2x + 2(20) find x when y = 1.5 m Substitute, then solve 3x + 2y = 12 find x when y = (x 10) P = 2W + 2L A = r2 Mar 3110:04 AM Mar 2810:01 AM Review: Creating Expressions A part time job pays $13.50 per hour. Create an expression to represent earnings. What's the difference between an expression and an equation? A car salesman earns $300 per week plus 5% commission on what she sells. Create an expression to represent her weekly earnings Oct 208:38 AM Oct 208:42 AM Problem Solving with Equations Creating Equations The goal? A part time job pays $13.50 per hour. Create an equation to represent earnings. To give yourself an equation to solve with one unknown. GIVEN the Equation A car salesman earns $300 per week plus 5% commission on what she sells. Create an equation to represent her weekly earnings Work on individual "pieces" to create match. "Sub & Solve" Oct 208:41 AM CREATE the Equation Start with word equation "Sub & Solve" Oct 33:26 PM 1 L24 Problem Solving with Equations.notebook Example #1: Using a Given or Known Equation (Shapes) The perimeter of the triangle is 35 m. Find the length of each side A circle has an area of 35 m2 What is the radius & diameter of the circle? March 12, 2015 A = r2 d = 2r 3x 2 2x + 3 P = a + b + c 3x + 4 Practice: Page 298 #20 Mar 2810:28 AM P = a + b + c + d Apr 110:08 AM Example #2: Creating Equation (Car Values) A company spent $308 700 on company cars in 2010. Each year, the total value of the cars depreciates by $38 100. a) Create an equation that represents the Total Value of the cars. b) If the company wants to ensure they keep $100 000 worth of value from the cars when they sell them all, how long should they keep the vehicles? Oct 178:28 AM Example #3: Working with Percentages (Commission) Oct 47:33 AM Jamie has two jobs in sales. She earns a commission of 2% of sales at a electronics store. Her commission at a clothing store is 4%. . What is commission? Commission is earned in jobs where your pay is based on a percentage of what you sell. a) Write an equation that models this situation (i.e. her total earnings). Example: A real estate agent earns 5% commission on the sale of a $250 000 house. How much did the agent earn? Earnings = 5% of $250 000 Earnings = 0.05(250 000) Earnings = $12 500. Apr 29:09 AM Apr 29:09 AM 2 L24 Problem Solving with Equations.notebook b) Last week she earned a total of $380. Her sales at the electronics store totaled $9500. What were her total sales at the clothing store? March 12, 2015 #7: A candy store is making up a mixture of chocolatecoated almonds and chocolatecoated raisins. The almonds cost $30 / kg and the raisins cost $10 / kg. The final value of the mixture is to be $150. The mix contains 7.5 kg of raisins. a) Write an equation that describes this situation "almonds cost $30 / kg" "raisins cost $10 / kg" C = Total cost of mix (in $) a = kg of almonds r = kg of raisins Total Cost = Cost of almonds + Cost of raisins C = 30a + 10r Practice: Page 295 #712 Apr 29:09 AM b) Solve the equation for the required mass of almonds. "The mix contains 7.5 kg of raisins" "The final value of the mixture is to be $150" C = 30a + 10r 150 = 30a + 10(7.5) 150 = 30a + 75 75 75 75 = 30a Oct 47:16 AM #8: Jamie builds chairs and tables in her shop. It takes her 3 h to make a chair and 7 h to make a table. Jamie works 60 h in a week. She made three tables last week. a) Write an equation that describes this situation "takes her 3 h to make a chair" "7 h to make a table" Hours Worked = Time for chairs + Time for tables H = 3c + 7t H = Time worked (in hours) c = # of chairs t = # of tables 2.5 = a 30 30 Therefore, there should be 2.5 kg of almonds to complete the mixture. Oct 77:20 AM b) Solve the equation to find the number of chairs she made last week. "She made three tables last week" "Jamie works 60 h in a week" #9: Christine has two jobs in sales. She earns a commission of 3% of sales at a clothing store. Her commission at the hardware store is 5%. Last week she earned $800. Her sales at the clothing store totalled $2500 a) Write an equation that describes this situation "earns a commission 3% of sales" H = 3c + 7t 60 = 3c + 7(3) 21 21 Oct 77:28 AM 60 = 3c + 21 "commission at the hardware store is 5%" Total Earnings = Clothing store + Hardware store E = 0.03c + 0.05h E = total earnings ($) c = clothing store h = hardware store 39 = 3c 3 3 Therefore, Jamie made 13 chairs last week. 13 = c Oct 77:30 AM Apr 110:11 AM 3 L24 Problem Solving with Equations.notebook b) Find her total sales at the hardware store by solving your equation "Her sales at the hardware store "Last week she earned $800" totalled $2500" E = 0.03c + 0.05h 800 = 0.03c + 0.05(2500) 125 800 = 0.03c + 125 125 675 = 0.03c March 12, 2015 #10: Nathan's boss sent him to the bank to get quarters and nickels. He has $250 to spend on the coins. Quarters are sold in rolls of 40. Nickels are sold in rolls of 40. Nathan bought 17 rolls of quarters. a) Write an equation that describes this situation "quarters are sold in rolls of 40" "nickels are sold in rolls of 40" Total Value = Value of quarters + Value of nickels V = Value of coins ($) q = # of rolls of quarters n = # of rolls of nickels V = 0.25(40)q + 0.05(40)n V = 10q + 2n 0.03 0.03 22 500 = c Therefore, Christine sold $22 500 at the hardware store last week. Apr 110:09 AM b) Find the number of rolls of nickels Nathan bought by solving your equation "Nathan bought 17 rolls of quarters" "He has $250 to spend on the coins" V = 10q + 2n 250 = 10(17) + 2n 170 170 250 = 170 + 2n 80 = 2n 2 Apr 110:12 AM Example #4: Given Limited Information (Investments ) How do Investments work? Investments will “return” or earn you a percentage of a larger amount you invest. Example: You invest $5 500 at a 3.5% return. How much did you earn on this investment? Earnings = 3.5% of $5 500 Earnings = 0.035(5 500) Earnings = $192.50 2 40 = n Therefore, Nathan bought 20 rolls of nickels. Apr 110:12 AM A broker invested $9 000. Part of the money was invested at 9% per annum. The rest was invested at 7% per annum. a) Create an equation that models this situation Apr 19:46 AM b) If the investments earned $650 in one year, how much was invested at each rate? Earnings = Amount @9% + Amount @ 7% E = 0.09x + 0.07y Earnings = Amount @ 9% + Amount @ 7% (0.09x) (0.07y) E = 0.09x + 0.07y 650 = 0.09x + 0.07y but we don't want 2 variables, so how else could we think of y? the amount invested @ 7% is whatever isn't invested @ 9% x + y = $9000 y = 9 000 x Mar 289:58 AM Apr 19:04 AM 4 L24 Problem Solving with Equations.notebook March 12, 2015 Earnings = Amount @ 9% + Amount @ 7% E = 0.09x + 0.07y 650 = 0.09x + 0.07 (9 000 x) 650 = 0.09x + 630 0.07x 650 = 0.02x + 630 y = 9 000 x = 9 000 1 000 20 = 0.02x = 8 000 1000 = x Therefore, $1 000 is invested @ 9%, and $8 000 is invested @ 7% Practice: Page 315 #17,18 Mar 2810:16 AM 5
© Copyright 2024