Julie goes with her friends to see Taylor Swift, queues up and buys 3 concert tickets and 1 signed T-shirt. She pays £110 but loses the receipt. The girl in front of Julie pays £50 for one ticket and one T-shirt. How much money did each ticket cost?

Whilst Julie has no receipt she can still find out how much each ticket costs because she has 2 equations (items bought by Julie as equation 1 and items bought by the girl in front for equation 2) for 2 unknown values (the cost of the ticket as the first unknown value and the cost of the t- shirt as the second unknown value). These can be put into a mathematical form.3x + y = £110 equation 1x + y = £50 equation 2(here x is the cost of a ticket in pounds and y is the cost of a t-shirt in pounds)subtract equation 2 from equation 1(3x + y) - (x + y) = £110 -£502x = £60divide both sides by 2x = £30The cost of a ticket is £30