Final answer:
To find the cost of 4 buckets and 6 spades, we need to set up and solve a system of equations using the given information.
Step-by-step explanation:
To solve this problem, let's represent the cost of a bucket as 'b' and the cost of a spade as 's'.
According to the information given, 2 buckets and 3 spades cost £8. This can be written as the equation 2b + 3s = 8.
Similarly, 4 buckets and 6 spades cost £x, which can be written as the equation 4b + 6s = x.
We can solve this system of equations by substitution or elimination. Let's use elimination:
Multiplying the first equation by 2, we get 4b + 6s = 16.
Subtracting this equation from the second equation, we get (4b + 6s) - (4b + 6s) = x - 16 -> 0 = x - 16 -> x = 16.
Therefore, the cost of 4 buckets and 6 spades is £16.