3 teas and 2 coffees have a total cost of £7.80 5 teas and 4 coffees have a total cost of £14.20 Work out the cost of one tea and the cost of one coffee.

We approach this question using algebra.Lets say the price of teas=x, and the price of coffees = ytherefore 2 equations can be written:3x+2y=7.805x+4y=14.20we now treat these equations as simultaneous equations. The easiest way to do this would be to multiply the first equation by 2 to make the number of coffees in each equation equal (4y). This gives us:6x+4y=15.605x+4y=14.20We can this subtract the second equation from the first equation to get rid of the y's and form one single equation:x=1.4. Therefore each tea is worth £1.40. To find the price of coffees we substitute 1.40 into either equation instead of x as we now know what this is:3(1.40)+2y=7.80.2y=3.6y=1.8. So the price of a coffee is £1.80