Simultaneous Equations REALLIFE SITUATIONS Objectives Apply life simultaneous

Simultaneous Equations REAL-LIFE SITUATIONS

Objectives: Apply life simultaneous equation in real-

Simultaneous Linear Equations Worked Example Question 1 The sum of two numbers is 130 and their difference is 38. Find them. Let x and y be the unknown numbers then: x + y = 130 eq 1 x - y = 38 eq 2 2 x = 168 x = 84 84 + y = 130 y = 46 The numbers are 84 and 46 1. Add equations. 2. Substitute in eq 1. 3. Check solutions 84 + 46 = 130 84 - 46 = 38

Simultaneous Linear Equations Worked Example Question 2 Five apples and 3 pears cost 86 pence. Seven apples and five pears cost £ 1. 30. Find the cost of each piece of fruit. Let a be the number of apples and p the number of pears then: 5 a + 3 p = 86 eq 1 7 a + 5 p = 130 eq 2 25 a + 15 p = 430 eq 3 21 a + 15 p = 390 eq 4 4 a = 40 a = 10 50 + 3 p = 86 3 p = 36 p = 12 1. eq 1 x 5 and eq 2 x 3 2. eq 3 - eq 4 3. Substitute in eq 1. 4. Check solutions 50 + 36 = 86 70 + 60 = 130 Apples cost 10 p and pears cost 12 p

Simultaneous Linear Equations Example Question 3 A slot machine takes only 20 p and 50 p coins. The machine contains a total of 140 coins worth £ 45. 10. How many of each type of coin are in the machine? Let t be the number of 20 p’s and f the number of 50 p’s then: t + f = 140 eq 1 20 t + 50 f = 4510 eq 2 20 t + 20 f = 2800 20 t + 50 f = 4510 30 f = 1710 f = 57 t + 57 = 140 t = 83 eq 2 There are 83, 20’p coins and 57, 50 p coins in the machine.

Q. I need to hire a car for a number of days. Below are the hire charges for two companies. Complete tables and plot values on the same graph. 160 180 200 240 300

Up to 2 days Swinton Over 2 days Arnold Total Cost £ Summarise data ! Who should I hire the car from? Arnold n to n wi S Days

Key steps 1. Fill in tables 2. Plot points on the same graph ( pick scale carefully) 3. Identify intersection point ( where 2 lines meet) 4. Interpret graph information. 5. Write the equation for each function. 6. Find another way to get the solution (point of intersection). 7. Interpret the point/s of intersection.

Portfolio (1 st Entry) – “My FUNCTIONS Storybook”

Choosing a mobile phone contract

The deals. . . Phone is free Phone is £ 45 £ 1 per min 50 p per min Phone is £ 100 Phone is £ 80 50 p per min 10 p per min

Let’s make a table. . . Number of minutes (£) Cost (£) 0 45 Phone is £ 45 10 50 50 p per min 20 55 30 60 40 65 50 70 60 75

80 Cost in pounds 70 60 Phone is £ 45 50 50 p per min 40 30 20 10 0 0 10 20 30 40 Minutes used 50 60 70