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 manipulate these equations. We can multiply the first equation by 2 to match the coefficients of $c$:

$6t + 4c = 15.60$

Now, we have:

1. $6t + 4c = 15.60$
2. $5t + 4c = 14.20$

Next, subtract the second equation from the first:

$6t + 4c - (5t + 4c) = 15.60 - 14.20$ This simplifies to: $t = 1.40$

Now that we have $t = 1.40$, we can substitute this value back into one of the original equations to find $c$. Let's use the first equation:

$3(1.40) + 2c = 7.80$ This simplifies to: $4.20 + 2c = 7.80$

Subtracting 4.20 from both sides gives: $2c = 3.60$

Dividing by 2: $c = 1.80$

Thus, we find:

• The cost of one tea is £1.40.
• The cost of one coffee is £1.80.