Paul buys three pens and one pencil for £11 while Sam buys four pens and two pencil for £16 - what is the price of pens and pencils?

Read the question and translate the information into equations.'Three pens and one pencil for £11' can be written as 3x + y = 11 where x = pens and y = pencils. 'Four pens and two pencils for £16' can be written as 4x + 2y = 16. We now have the equations 3x + y = 11 and 4x + 2y = 16. We want to manipulate one of the equations so that we either have the same x value or the same y value as this will let us subtract one equation from the other, meaning we will have an equation in only one variable which can be solved. In this case we can divide both sides of equation 2 by two, so '4x+2y = 16' becomes '2x+y=8'. Then we have 3x + y =11 and 2x + y = 8. At this point we have the same y value in each equation, so we can subtract equation 2 from equation 1: (3x + y) - (2x + y) = 11 - 8 = 3 so 3x - 2x + y - y = 3x = 3. At this point we have solved the equations for x, so we can choose an equation to use this x value to solve y. Using equation one, we have 3x + y = 11. We can substitute our solution x = 3 into this equation so 3(3) + y = 11 so 9 + y = 11 so y = 11 - 9 = 2. So the solution is x = pens = £3 and y = pencils = £2.