5) 6) 7) 8) More help: Forming equations Example 8: Find three consecutive numbers so that their sum is 96. Solution: Let the first number be then the second is + 1 and the third is + 2. n, n n Therefore + (n + 1) + (n + 2) = 96 n 3n + 3 = 96 3n = 93 = 31 n So the numbers are 31, 32 and 33. Exercise D: 1) Find 3 consecutive even numbers so that their sum is 108. 2) The perimeter of a rectangle is 79 cm. One side is three times the length of the other. Form an equation and hence find the length of each side. 3) Two girls have 72 photographs of celebrities between them. One gives 11 to the other and finds that she now has half the number her friend has. Form an equation, letting be the number of photographs one girl had at the beginning. n Hence find how many each has now. Chapter 3: SIMULTANEOUS EQUATIONS An example of a pair of simultaneous equations is 3x + 2y = 8 5x + = 11 y In these equations, and stand for two numbers. We can solve these equations in order to find the x y values of and by eliminating one of the letters from the equations. x y
5) 6) 7) 8) More help: Forming equations Example 8: Find three consecutive numbers so that their sum is 96. Solution: Let the first number be n, then the second is n + 1 and the third is n + 2. Therefore n + (n + 1) + (n + 2) = 96 3n + 3 = 96 3n = 93 n = 31 So the numbers are 31, 32 and 33. Exercise D: 1) Find 3 consecutive even numbers so that their sum is 108. 2) The perimeter of a rectangle is 79 cm. One side is three times the length of the other. Form an equation and hence find the length of each side. 3) Two girls have 72 photographs of celebrities between them. One gives 11 to the other and finds that she now has half the number her friend has. Form an equation, letting n be the number of photographs one girl had at the beginning. Hence find how many each has now. Chapter 3: SIMULTANEOUS EQUATIONS An example of a pair of simultaneous equations is 3x + 2y = 8 5x + y = 11 In these equations, x and y stand for two numbers. We can solve these equations in order to find the values of x and y by eliminating one of the letters from the equations.