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. - Edexcel - GCSE Maths - Question 11 - 2017 - Paper 1

To eliminate one variable, we can multiply the first equation by 2 to make the coefficients of $c$ in both equations the same:

$6t + 4c = 15.60$

Now we can subtract the second equation from this modified first equation:

$(6t + 4c) - (5t + 4c) = 15.60 - 14.20$

This simplifies to:

$t = 1.40$

Now that we know the cost of one tea ($t = 1.40$), we can substitute this back into one of the original equations to find the cost of coffee. Let's use the first equation:

$3(1.40) + 2c = 7.80$

This gives:

$4.20 + 2c = 7.80$

Subtracting $4.20$ from both sides:

$2c = 3.60$

Dividing both sides by 2 gives:

$c = 1.80$

The final costs are:

• Cost of one tea: £1.40
• Cost of one coffee: £1.80