8 (a) A shop sells shirts for $x and jackets for $(x + 27). The shop sells 4 shirts and 3 jackets for a total of $194.75 . Write down and solve an equation to find the cost of one shirt. $ ................................................ [3] (b) Solve the simultaneous equations. You must show all your working. x2+4y = 37 5x+y =-8 x = ..................... , y = ..................... x = ..................... , y = ..................... [5] © UCLES 2023 0580/43/M/J/23 15 (c) A solid cylinder has radius x and height 6x. A sphere of radius r has the same surface area as the total surface area of the cylinder. 7 Show that r2 = x2. 2 [The surface area, A, of a sphere with radius r is A = 4rr2.] [4] © UCLES 2023 0580/43/M/J/23 [Turn over 16