Answer: tea: £0.5
coffee: £1.25
Step-by-step explanation: Let's represent the cost of tea as t and the cost of coffee as c.
Elliot bought two coffees and one tea and paid £3, i.e.,
t + 2c = 3
Elise paid £2.25 for two teas and one coffee, or:
2t + c = 2.25
The system of equations to solve are
t + 2c = 3 (1)
2t + c = 2.25 (2)
One way to solve this system is by substitution:
t = 3 - 2c (3)
Using (3) to substitute in (2):
2(3 - 2c) + c = 2.25
6 - 4c + c = 2.25
- 3c = - 3.75
c = 1.25
Now, to determine t, we can use (1) or (3).
As it is easier, we use (3):
t = 3 - 2(1.25)
t = 0.5
The cost of 1 coffee and 1 tea is £1.25 and £0.5, respectively.