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.

Firstly we need to set up a simultaneous equation. 3t +2c =7.80 and 5t +4t = 14.20 Rearrange the first equation to find c on its own. 2c = 7.80 - 3t, c= (7.80 - 3t) / 2Then put the new value of c into the second equation. 5t + 4( (7.80-3t)/2) =14.20Next we need to expand the brackets in the equation. Since 4 divided by 2 is 2 we can say 5t+ 2(7.80-3t) =14.20 5t + 15.60 -6t = 14.20-t = 14.20-15.60-t= -1.40Multiply both sides by -1t= £1.40Next all we have to do is plug in the value of t into one of the original equations to find the value of c.c= (7.80 -3t)/2 c= (7.80 -3(1.40))/2c= (7.80- 4.20)/2c=3.60/2c= 1.80Therefore the cost of one tea is £1.40 and the cost of one coffee is £1.80.